University of Gour Banga

(Established under West Bengal Act XXVI of 2007)

N.H.-34(Near Rabindra Bhawan), P.O.:Mokdumpur Dist.: Malda,

West Bengal, Pin-732103

M.Sc. in Physics

Two Years (Four Semesters) Syllabus

Main Feature of the Syllabus M.Sc. in Physics

Semester Paper Code Paper Name Theory Marks

Time Internal Assessment

Marks

Time Total Marks

I

PAPER 101 Mathematical Methods 40 2.00 Hr 10 30.00 Min 50 PAPER 102 Classical Mechanics 40 2.00 Hr 10 30.00 Min 50 PAPER 103 Quantum Mechanics-I 40 2.00 Hr 10 30.00 Min 50 PAPER 104 Classical Electrodynamics 40 2.00 Hr 10 30.00 Min 50 PAPER 105 General Practical 40 3.00 Hr 10 30.00 Min 50

Total 250

II

PAPER 201 Statistical Mechanics 40 2.00 Hr 10 30.00 Min 50 PAPER 202 Relativity and Nonlinear Dynamics 40 2.00 Hr 10 30.00 Min 50 PAPER 203 Quantum Mechanics-II 40 2.00 Hr 10 30.00 Min 50 PAPER 204 Electronics 40 2.00 Hr 10 30.00 Min 50 PAPER 205 Electronics Practical 40 3.00 Hr 10 30.00 Min 50

Total 250

III

PAPER 301 Condensed Matter Physics 40 2.00 Hr 10 30.00 Min 50 PAPER 302 Atomic and Molecular Spectroscopy 40 2.00 Hr 10 30.00 Min 50 PAPER 303 Plasma Physics 40 2.00 Hr 10 30.00 Min 50 PAPER 304 Optics Practical 40 3.00 Hr 10 30.00 Min 50 PAPER 305 Computer Practical 40 3.00 Hr 10 30.00 Min 50

Total 250

IV

PAPER 401 Advanced Optics and Elective Subject 40 2.00 Hr 10 30.00 Min 50 PAPER 402 Nuclear and Particle Physics 40 2.00 Hr 10 30.00 Min 50 PAPER 403 Special Paper 40 2.00 Hr 10 30.00 Min 50 PAPER 404 Special Practical 40 3.00 Hr 10 30.00 Min 50 PAPER 405 Project 40 3.00 Hr 10 30.00 Min 50

Total 250

Grand Total

1000

Special Paper: A: Computational Physics B: Advanced Electronics

Detailed Syllabus

Semester I PAPER 101: Mathematical methods

1. Functions of a complex variable: Di_erentiability. Cauchy-Riemann equations. Harmonic functions. Analytic functions. Entire functions. Multiple-valued functions. Branch points and branch cut. Riemann surfaces. Complex integration. Contour integrals. Darboux inequality. Cauchys theorem. Cauchys integral formula. Liouvilles theorem. Moreras theorem. Taylor and Laurent series. Singular points and their classification. Residue theorem. Jordans lemma. Application of residue theorem to the evaluation of definite integrals and the summation of infinite series. Integrals involving branch point singularity. Analytic continuation. Schwarz reflection principle. (10L)

2. Fourier integral theorem. Fourier and Laplace transforms. Inverse transforms. Persevall’s theorem. Convolution theorem. Solution of ordinary and partial di_erential equations by transform methods. (4L)

3. Di_erential equations and Greens function: Second order Linear di_erential Equations methods of solution; Sturm-Liouville problem. Legendre, Bessel, Hermite and Laguerre functions and polynomials: Di_erential Equations, series solutions, recursion relations, orthonormality, position of zeroes, connection with Sturm-Liouville problem. Partial Di_erential equations methods of solution: separation of variables method, eigenfunction expansion method, integral transform method. Greens function: definition and properties; methods of computation: direct computation, eigenfunction expansion method, integral transform method. (7L)

4. Tensor analysis: Coordinate transformations, scalars, definition of tensors, contravariant, covariant and mixed tensors, addition of tensors, inner and outer products, contraction, symmetric and anti-symmetric tensors, quotient law, Kronecker delta and Levi-Civita symbols, Euclidean and Riemannian space, fundamental metric tensor, conjugate tensor, associate, contravariant and covariant vectors. (4L)

5. Group theory: a) Groups. Definition and examples. Order of a group. Multiplication table. Rearrangement

theorem. Generators of a finite group. Conjugate elements and classes. Subgroups. Cayleys theorem. Cosets. Lagranges theorem. Direct product of groups. Invariant subgroups. Factor group. Isomorphism and homomorphism. Permutation groups. Distinct groups of a given order. Cyclic and noncyclic groups. (5L)

b) Group representations. Definition of representation. Faithful and unfaithful representations. Equivalent representations. Invariant subspaces and reducible representations. Reducibility of a representation. Irreducible representation. Schurs lemmas.Orthogonality theorem. Construction of some groups (C2v;C3v; D2h) (5L)

c) Discrete, continuous, and mixed continuous groups. Topological and Lie groups. Axial rotation group SO(2). Rotation group SO(3). Special unitary groups SU(2), SU(3) and their applications in physics. (5 L)

6. Tutorials (5L)

Books Recommended:

1. M. R. Spiegel: Theory and Problems of Complex Variables (Schaums outline series). 2. G. Arfken: Mathematical Methods for Physicists (Academic Press). 3. J. Mathews and R. I. Walker :Mathematical Methods of Physics (Benjamin). 4. P. Dennery and A. Krzywicki: Mathematics for Physicists (Harper and Row).

5. L. Andrews and B. Shivamoggi,: Integral Transforms for Engineers (PHI). 6. M. Tinkham: Group Theory and Quantum Mechanics (McGraw-Hill) 7. A. Joshi: Matrices and Tensors (Wiley Esstern). 8. A. Joshi: Group Theory (Wiley Eastern). 9. M. Hammermesh: Group Theory (Dover)

PAPER 102: Classical Mechanics

1. Review of Lagrangian and Hamiltonian formalisms: Legendre transforms. Hamiltons function and Hamiltons equations of motion. Simple applications. Lagrangian and Hamiltonian of relativistic particles. Action. Principle of least action. Hamiltons principle. Maupertuis principle. Euler Lagrange equations of motion from Hamiltons principle. Hamiltons equations of motion from Hamiltons principle. Noethers theorem. (9L)

2. Central force: Two body central force problem. classification and stability of orbits. condition for closure. integrable power laws. Keplers problems. orbits of artificial satellites. Virial theorem. Scattering in a central force field. Rutherford scattering. three body problem. (5L)

3. Rigid body motion:Kinematics of rigid body motion. Euler angles. Eulers equations of motion. Torque free motion of a rigid body. heavy symmetrical top. Fast and sleeping top. (5L)

4. Small oscillation: Formulation of the problem of small oscillations. The eigen-value equation and the principal axis transformation. Frequencies of free vibration and normal coordinates. Forced oscillations and the effect of dissipative forces. (5L)

5. Canonical transformations: Examples. Integral invariants of Poincare. Lagrange and Poisson brackets as canonical invariants. The equations of motion in Poisson bracket notation. Infinitesimal contact transformation. Constants of the motion. Symmetry properties. Angular momentum Poisson bracket relations. Liouvilles theorem. (9L)

6. Hamilton-Jacobi (HJ) theory: Hamilton-Jacobi equations for Hamiltons principal and characteristic functions. The harmonic oscillator problem by Hamilton-Jacobi method. Separation of variables in the Hamilton-Jacobi equation. Action-angle variables. Periodic motion.The Kepler problem in action-angle variables. Passage from classical to quantum mechanics. (9L)

7. Continuous system and fields: Clasical Lagrangian and Hamiltonian density, equation of motion, conservation theorems. (3L)

8. Tutorials. (5L)

Books Recommended:

1. H. Goldstein, C. Poole and J. Safko: Classical mechanics (Pearson). 2. S. McCuskey: Introduction to advanced dynamics (Addison-Wesley). 3. L. Landau and E. Liftshitz: Mechanics (Addison-Wesley). 4. K.C. Gupta: Classical Mechanics ( New Age Books). 5. N. Rana and P. Joag: Classical Mechanics (Tata McGraw-Hill). 6. S. Sinha: Classical Mechanics (Narosa). 7. Marion and Thomtron: Classical Dynamics of Particles and Systems Third Edition, Horoloma Book

Jovanovich College Publisher. 8. P.V.Panat: Classical Mechanics, Narosa Publishing Home, New Delhi. 9. Introduction to Classical Mechanics by R.G.Takawale and P.S.Puranik, Tata Mc-Graw Hill

Publishing Company Limited, New Delhi.

PAPER 103: Quantum Mechanics I

1. Reviews of introductory discussions on Schrodinger equation and relevant topics.(3L) 2. Formalism of quantum mechanics. Axiomatic definition. Vector spaces; linear independence, bases,

dimensionality. Inner product, Gram-Schmidt orthogonalisation. Linear operators. Representation of linear transformations and change of base. Eigenvalues and eigenvectors. Functions of a matrix. Cayley- Hamilton theorem. Commuting matrices with degenerate eigenvalues. Orthonormality of eigenvectors. Hilbert space. Kets, bras and operators, Base kets and matrix representation. Hermitian operator. Eigenkets as base kets. Orthogonality.The superposition and completeness of eigenstates. Postulates of quantum mechanics. Observable and results of its measurement. The generalized uncertainty relation. Expectation values of dynamic variables. Commutators and operator algebra. Non-commutating observables. Complete set of commuting observables. Change of basis. Unitary operators Discrete and continuous bases. Coordinate and momentum representations. Quantum Dynamics. Schrodinger, Heisenberg and interaction pictures. Evolution operator. Linear harmonic oscillator by Schrodinger equation, Heisenberg equation and Dirac operator method. Coherent states. (12L)

3. Time-independent Schrodinger equation in one dimension. The free particle. The infinite square well. The delta-function and periodic delta function potential. The finite square well. Transmission coefficient. Schrodinger equation in three dimensions. Schrodinger equation in spherical coordinates. Orbital angular momentum. Eigenvalue problem for angular momentum. Spherical harmonics. The rigid rotator. The spherical well with impenetrable walls. Spherical square well potential. Coulomb potential. The hydrogen atom problem. Parity of wavefunctions. (8L)

4. Approximation methods. Time-independent perturbation theory for non-degenerate and degenerate states. Applications to anharmonic oscillator, Stark effect in hydrogen atom. Variational methods. Application to the ground state of delta function potential, helium atom, Hydrogen molecule ion. The WKB approximation. General form. Application to the theory of alpha decay. Connection formulas. (9L)

5. Time-dependent perturbation theory. Constant and harmonic perturbations. Fermis golden rule. Sudden and adiabatic approximations. Interaction of an atom with electromagnetic wave. Transition probability and Electric dipole radiation. (5L)

6. Identical particles. Symmetry under interchange. Wave functions for bosons and fermions. Slater determinant. (3L)

7. Tutorials. (5L)

Books Recommended: 1. P. A. M. Dirac: Principles of Quantum Mechanics(Oxford). 2. L. Schi_: Quantum Mechanics (McGraw-Hill). 3. E. Merzbacher: Quantum Mechanics (John Wiley and sons). 4. D. Gri_ths: Introduction to Quantum Mechanics (Pearson Education). 5. Bransden and Joachain: Quantum Mechanics. 6. A. K. Ghatak and S. Lokanathan: Quantum Mechanics (Macmillan India Ltd.). 7. J. Sakurai: Modern Quantum Mechanics (Addison-Wesley). 8. C. Cohen-Tannoudji et al : Quantum Mechanics Vol I and II (John Wiley). 9. R. L. Libo_: Introductory Quantum Mechanics (Pearson Education). 10. R. Robinett: Quantum Mechanics (Oxford University Press). 11. M. Bellac: Quantum Physics (Cambridge University Press).

PAPER 104: Classical Electrodynamics

1. Review of electrostatics and magnetostatics: Formal solution of the electrostatic boundary value problem with Greens function. Boundary value problems. Multipole expansion of fields and potentials. Electrostatics of macroscopic media. (4L)

2. Electromagnetic induction: Fundamental equations. Maxwells equations. Electromagnetic waves in conducting and nonconducting media. Frequency dependence of permitivity. wave guides. (4L)

3. Potentials and fields: Gauge transformations Lorentz and Coulomb gauges; Poynting vector. The inhomogeneous wave equation - Greens function, retarded and advanced potentials. Fields and radiation of a localized oscillating source. Multipole expansion of scalar and vector potentials; radiation fields, dipole radiation. Lienerd-Weichert potentials; the fields of a uniformly moving charge. Radiation from an accelerated charge. Angular distribution of the emitted radiation; Larmors formula and its relativistic generalization; special cases of acceleration; parallel and perpendicular to velocity. Bremsstrahlung, Cerenkov radiation, radiation reaction. (12L)

4. Relativistic Electrodynamics: Tensors in minkowski space, Electromagnetic field tensor, Covariance of electrodynamics, Transformation of electromagnetic field. Relativistic Lagrangian and Hamiltonian and Hamiltonian of a charged particle in an electromagnetic field. Lagrangian for electromagnetic field; stress tensors, conservation laws (12L)

5. Scattering from a free electron. Thomson scattering. Scattering from a bound electron. Rayleigh scattering. Absorption of radiation by a bound electron. Normal and anomalous dispersion. Lorentz electromagnetic theory. (8 L)

6. Tutorials. (5L)

Books Recommended: 1. W. Panofsky and M. Phillips: Classical Electricity and Magnetism (Addison- Wesley). 2. D. Griffith: Electrodynamics (Prentice Hall India). 3. J. Jackson: Classical Electrodynamics (Wiley Eastern). 4. J. Marion: Classical Electromagnetic Radiation (Academic Press). 5. J. Schwinger: Classical Electrodynamics. 6. Ashok Das: Classical Electrodynamics.

PAPER 105:General Practical

List of General Experiments:

1. Study of temperature dependence of resistivity for a given semiconductor using four probe setup and determine its energy band gap.

2. Determination of Saturation Magnetization, Retentivity and Coercivity of given Ferromagnetic samples Using hysteresis loop tracer.

3. Determination of Hall Coe_cient of a given semiconductor sample using variable DC magnetic field. 4. Study of the variation of Hall Coe_cient of a given extrinsic semiconductor as a function of

temperature using Temperature dependence Hall e_ect setup. 5. Determination of the specific charge of an electron by the solenoidal lens method / modified

Thompsons method. 6. Study of Lissajous figures and calibrate an Audio Frequency Oscillator by phase change and direct

method. 7. Determination of the velocity of ultrasonic wave in a given liquid for a given frequency using multi

frequency ultrasonic interferometer /liquid grating method. 8. Demonstration of discrete electronic energy levels by Franck and Hertz experiment setup. 9. Determination of the Lande g factor for the DPPH sample using electron spin resonance setup. 10. Study of temperature dependence of the Dielectric Constant and determination of the Curie-point of a

ferro-electric Material. 11. Determination of electron density and electron temperature of a plasma by single/ double probe

method

Semester II PAPER 201: Statistical Mechanics

1. Scope and aim of statistical mechanics. Transition from thermodynamics to statistical mechanics. Review of the ideas of phase space, phase points, and ensemble. Density of phase points. Liouvilles equation and Liouvilles theorem. (3L)

2. Stationary ensembles: Micro canonical, canonical and grand canonical ensembles. Partition function formulation. Fluctuations in energy and particle number. Equilibrium properties of ideal systems: ideal gas, Harmonic oscillators, rigid rotators. Para magnetism, concept of negative temperature. (10L)

3. Density matrix: Idea of quantum mechanical ensemble. Statistical and quantum mechanical approaches. Pure and mixed states. Density matrix for stationary ensembles. Application to a free particle in a box, and an electron in a magnetic field. Density matrix for a beam of spin 1/2 particles. Construction of the density matrix for different states (pure and mixture) and calculation of the polarization vector. (8L)

4. Distribution functions. Bose-Einstein and Fermi-Dirac statistics. General equations of state for ideal quantum systems. (4L)

5. Ideal quantum systems: (a)Properties of ideal Bose gas. Bose-Einstein condensation. Transition in liquid He4, Superfluidity in He4. Photon gas. Plancks radiation law. Phonon gas. Debyes theory of specific heat of solids. (b) Properties of ideal Fermi gas: Review of the thermal and electrical properties of an ideal electron gas. Landau levels, Landau diamagnetism. White dwarf and Neutron stars. (10L)

6. Strongly interacting systems. Ising model. Idea of exchange interaction and Heisenberg Hamiltonian. Ising Hamiltonian as a truncated Heisenberg Hamiltonian. Exact solution of one-dimensional Ising system (Matrix method). Bragg-Williams approximation (Mean field theory) and the Bethe-Peierls approximation. (6L)

7. Phase transition: General remarks. Ehrenfest’s classification, Phase transition and critical phenomena. Critical indices. Landaus order parameter theory of phase transition. (4L)

8. Thermodynamic fluctuations. Spatial correlations in a fluid. Brownian motion: Einstein-Smoluchowskis theory. (5L)

9. Tutorials. (5L) Books Recommended:

1. R. Pathria: Statistical Mechanics 2. K. Huang: Introduction to Statistical Mechanics 3. S. Salinas: Introduction to Statistical Mechanics. 4. F. Reif: FundamentaL of Statistical and Thermal Physics. 5. R. Kubo: Statistical Mechanics. 6. S. Bowley: Introductory Statistical Mechanics (Oxford University Press). 7. L. Kadano_: Statistical Mechanics (World Scientific). 8. Landau and Liftshitz: Statistical Mechanics. 9. B. B. Laud: Statistical Mechanics.

PAPER 202: Relativity and Nonlinear Dynamics

1. Special Theory of Relativity: Lorentz transformation; Dopler effect, 4-vector(time space and light like), 4-velocity and acceleration; 4-momentum and force. Minkowski space and metric. Relativistic invariants and kinematics: Decay, elastic collision and reaction. Lagrangian formulation of relativistic mechanics. covariant Lagrangian formulation. (8L)

2. General theory of relativity: Review of tensor analysis. inclination of two vectors orthogonality, areas and volumes, raising and lowering of indices, Christo_el symbols and teir transformations; intrinsic and covariant di_erentiations, Riemann Christo_el tensors, Bianchi identities, curvature tensors, di_erential equation of geodesics, parallel transports, anti-parallel curves, condition of flatness, Ricci tensor, Einstein tensor. Inconsistence of Newtonian gravitation with special theory of relativity; principles of equivalence and general covariance; Einsteins field equations; Schwarzschild solution; geodesics of Schwarzschild solution; singularity, event horizon and black holes, Birkhoffs theorem; experimental tests- perihelion motion of a planet, bending of light and gravitational red shift; (10L)

3. Nonlinear Dynamics: Idea of Nonlinearity. Framework for the study of dynamics in state space. Autonomous and nonautonomous systems. The no-intersection theorem. Dissipative systems and attractors. One-dimensional state space. Fixed points and stability. Linearization near fixed points. Lyapunov exponent. Trajectories in a one-dimensional state space. Phase portrait. (6 L)

4. Two-dimensional state space. Brusselator model. Dynamics and complex characteristic values. Dissipation and the divergence theorem. Jacobian matrix for characteristic values. Limit cycles. Poincar sections and the stability of limit cycles. Poincar-Bendixson theorem. (6 L)

5. Bifurcations. Saddle-node and repellor-node bifurcations. Supercritical and subcritical pitchfork bifurcations. Bifurcations in two dimensions. Limit cycle bifurcations. Hopf bifurcation. (5L)

6. Three-dimensional state space. Routes to chaos. Period doubling. Quasi-periodicity. Intermittancy. Lorenz model, Simple properties of the Lorenz equations, Introduction to chaos. Lyapunov exponents.(5L)

7. Tutorials. (5L)

Books Recommended: 1. H. Goldstein, C. Poole and J. Safko: Classical mechanics (Pearson). 2. McCuskey: Introduction to advanced dynamics (Addison-Wesley). 3. K.C. Gupta: Classical Mechanics ( New Age Books). 4. N. Rana and P. Joag: Classical Mechanics (Tata McGraw-Hill). 5. S. Sinha: Classical Mechanics (Narosa). 6. S. Banerji and A. Banerjee: Special Theory of Relativity. 7. A. Roychaudhuri, S. Banerjee and A. Banerjee: General Relativity, Astrophysics and Cosmology

(Springer-Verlag). 8. S. Banerji and A. Banerjee: General Relativity and Cosmology (ELevier) 9. R. Hilborn: Chaos and Nonlinear Dynamics (Oxford University Press). 10. S. Strogatz: Nonlinear Dynamics and Chaos (Addison-Wesley). 11. J. Bhattacharjee: Nonlinear Dynamics Near and Far From Equilibrium (Hindustan

PAPER 203: Quantum Mechanics II

1. Generalised angular momentum. Infinitesimal rotation. Generator of rotation. Commutation rules. Matrix representation of angular momentum operators. Spin. Pauli spin matrices. Eigenspinors. Electron in static magnetic field. Larmor precession. Electron in an oscillating magnetic field. Addition of two angular momenta. Simple examples. Clebsch-Gordan co-efficients. Recursion relations. (8 L)

2. Discrete and continuous space-time symmetries. Invariance principles and conservation laws. Space translation. Time translation. Space rotation. Irreducible spherical tensor operators. Wigner-Eckert theorem. Space inversion. Time reversal. Kramers degeneracy. (5 L)

3. Scattering theory. Scattering amplitude. Di_erential and total cross sections. Integral equation for potential scattering. Greens function. Born approximation and its validity. Yukawa potential. Rutherford scattering formula. Method of partial waves. Phase shifts. Optical theorem. Scattering by a hard sphere. (6 L)

4. Relativistic quantum mechanics. The Klein-Gordon equation. Covariant notation. Probability density. Negative energy solution. The Dirac equation. Properties of the Dirac matrices. The Dirac particle in an electromagnetic field. The spin and magnetic moment of the electron. (8 L)

5. Covariant form of the Dirac equation. Lorentz covariance. Rotation, parity and time reversal operations on the Dirac wavefunction. The 5 matrix and its properties. Plane wave solutions of the Dirac equation and their properties. Energy and projection operators. Diracs hole theory. (4L)

6. Non-relativistic limit of the Dirac equation. Large and small components. Spin-orbit interaction from Dirac equation. Foldy-Wouthuysen transformations for a free particle and for a particle in a field. Electon in a central electrostatic potential. (4L)

7. Concept of field. Lagrangian dynamics of classical fields. Euler-Lagrange equation. Lagrangians and equations of motion of fundamental fields. Noethers theorem. Conserved currents and charges. Energy-momentum tensor and energy of fields. Introductory idea about second quantization. Example-Schrödinger equation(4 L)

8. Tutorials. (5L)

Books Recommended: 1. E. Merzbacher: Quantum Mechanics (John Wiley and sons). 2. D. Gri_ths: Introduction to Quantum Mechanics (Pearson Education). 3. A. K. Ghatak and S. Lokanathan: Quantum Mechanics (Macmillan India Ltd.). 4. J. Sakurai: Modern Quantum Mechanics (Addison-Wesley). 5. C. Cohen-Tannoudji et al : Quantum Mechanics VoL I and II (John Wiley). 6. R. L. Libo_: Introductory Quantum Mechanics (Pearson Education). 7. J. Bjorken and S. Drell: Relativistic Quantum Mechanics (McGraw-Hill). 8. J. Sakurai: Advanced Quantum Mechanics (Addison-Wesley). 9. A. Lahiri and P. Pal: A First Book of Quantum Field Theory (Narosa). 10. T-Y Wu and W-Y Hwang: Relativistic Quantum Mechanics and Quantum Fields (Allied Publishers). 11. C. Itzyksen and J. Zuber: Quantum Field Theory (McGraw-Hill). 12. L. Ryder: Quantum Field Theory (Cambridge University Press).

PAPER 204: Electronics

1. Networks: Review of network theorems. Driving point impedance and admittance, Fosters reactance theorems. Canonic networks. Filter circuits. Active and passive filters. LPF, HPF, BPF and BRF type constant-k prototype filters. Attenuators. (4 L)

2. Transmission line theory: Distributed parameters. Primary and secondary line constants; Telegraphers equation. Reflection co-efficient and VSWR. Input impedance of loss-less line. Distortion of em wave in a practical line. Smith chart. (5 L)

3. Semiconductor physics: Carrier concentration. Fermi levels of intrinsic and extrinsic semi-conductors. Bandgap. Direct and indirect gap semiconductors. p-n junction physics. Junction breakdown. Heterojunction. Characteristics of some semiconductor devices: LED, Solar cell, Tunnel diode, Gunn diode and IMPATT. SCR; Unijunction transistor (UJT). Programmable Unijunction transistor (PUT).(10 L)

4. Active Circuits: Transistor amplifiers. Basic design consideration. High frequency effects. Video and pulse amplifier. Tuned amplifier. Nonlinear amplifiers using op-amps. regenerative comparators. Precision rectifiers. Op-amp based function generators. (8 L)

5. Communication electronics: Principles of analog modulation- linear and exponential types. Generation of transmitted carrier and suppressed carrier type AM signals. Principles of FM and PM signal generation. Principles of detection modulated signals. Modulation techniques in some practical communication systems. AM and FM radio. (8 L)

6. Digital circuits: Logic simplification using Karnaugh maps. SOP and POS design of logic circuits. Multiplexure and demultiplexure. RS, JK and MS-JK flip-flops. transformation of flip-flops. Registers and counters. design of counters. ADC and DAC circuits. Basics of Microprocessors and microcontrollers (10 L)

7. Tutorials. (5L) Books Recommended:

1. J. Ryder: Networks Line and Fields (PHI). 2. Frazier: Telecommunications. 3. Zee: Physics of Semiconductor Devices (Wiley). 4. Milman and Grable: Microelectronics(Tata McGraw-Hill). 5. Chattopadhyay and Rakshit: Electronic Circuit Analysis (New Age International). 6. Malvino and Bates: Electronics Principles. 7. Anand Kumar: Fundamentals of Digital circuits 8. Malvino and Brown: Digital computer electronics

PAPER 205: Electronics Practical

List of Electronics Experiments: 1. Experiment with Op-amp.

(i) To design and study an amplifier with an Op-amp. (ii) To design and study an oscillator with an Op-amp. (iii)To design and study a voltage follower circuit with an Op-amp

2. Construct a sawtooth wave generator using UJT for different frequencies. Determine VP, VV and , symbols having the usual meanings. For a fixed C, vary R (5 values) and Draw the TR graph. Plot the theoretical TR graph on the same graph paper. Obtain two such sets.

3. Construct a sawtooth wave generator using UJT for different frequencies. Determine VP, VV and , symbols having the usual meanings. For a fixed R, vary C (5 values) and Draw the TC graph. Plot the theoretical TC graph on the same graph paper. Obtain two such sets.

4. Design an astable multivibrator with two transistors for a fixed given frequency (1.0 KHz). Assume Vc(sat)=0.2 volt, Ic(sat)=5 mA, hFE(min)=100 and VBE(sat)=0.6 volt. Compare the experimentally obtained frequencies with the required theoretical values. Using this multivibrator design a VCO and draw its transfer characteristics. From this plot calculate the VCO sensitivity.

5. Design the following RC passive filters: (a) Low Pass (LPF) (b) High pass (HPF) (C)Band Pass(BPF). Draw separate frequency response curves and compare the theoretical and experimental results for each.

6. Design the following RC active filters: (a) Low Pass (LPF) (b) High pass (HPF) (C)Band Pass (BPF). (D) Band Stop. Draw separate frequency response curves and compare the theoretical and experimental results for each.

7. Design the following using NAND gates only: (a) SR FlipFlop with the provision of clock (enable input). Study the output for different combinations of S and R. (b) Convert the above to clocked D Flip Flop. (c) Design a clocked JK FlipFlop and study the results of different combinations of J, K and clock. Note the drawback of the experimental circuit, if any and suggest a suitable circuit to remove the drawback with proper explanation.

8. (a) Study the performance of AM modulator circuit by considering three different values of

modulating signal amplitude and frequency. Determine modulation index in each case. (b) Study the performance of AM demodulator circuit by considering three different values of

modulating signal amplitude and frequency. Write down your observations clearly. 9. Design a transistor CE amplifier of midband gain 50 and study its performance in the following way:

(a) Test the linearity of input output variations of a voltage signal of suitable fixed frequency and show it graphically.

(b) For fixed amplitude of input ac signal within the linear region, study the frequency response with an external bypass capacitor at the output. Plot the gain frequency graph and determine the bandwidth of the amplifier.

10. Simple microprocessor (8085 or 8086) programs: (a) Average of some numbers (b) Testing even/odd (c) Addition of 2byte numbers (b) Multiplication of two 8bit numbers

11. Study of voltage controlled oscillator using IC-566.

Semester III PAPER 301: Condensed Matter Physics

1. Crystalline and amorphous solids: The crystal lattice. Basis vectors. Unit cell. Symmetry operations.

Point groups and space groups. Plane lattices and their symmetries. Three dimensional crystal

systems. Miller indices. Studdy of some simple crystal structures. X-ray diffraction. Laue theory.

Braggs law. Reciprocal lattice. Atomic scattering factor. Experimental methods of x-ray diffraction.

Comparative study of X-ray, neutron and electron diffraction. (10L)

2. Types of bonding: The van der Waals bond. Cohesive energy of inert gas solids. Ionic bond. Cohesive

energy and bulk modulus of ionic crystals. Madelung constant. The covalent bond. Metallic bond.

(4L)

3. Vibrations of one-dimensional monatomic and diatomic lattices. Infrared absorption in ionic crystals

(one-dimensional model). Normal modes of harmonically vibrating solids. Phonons. Frequency

distribution function. Debyes theory of lattice specific heat. Anharmonic effects. (6 L)

4. Quantized free electron theory. Fermi energy, wave vector, velocity and temperature. Density of

states in one, two and three dimensions. Electronic specific heat. Pauli spin paramagnetism. Free

electron theory of electrical and thermal conductivity. AC conductivity and optical properties. Plasma

oscillations. Hall effect. Hall coefficient in one- and two- band models. (8 L)

5. Magnetic and optical properties of solids: Diamagnetism, Langevin equation. Quantum theory of

paramagnetism. Curie law. Hund’s rules. Paramagnetism in rare-earth and iron-group ions.

Elementary idea of crystal field effects. Ferromagnetism. Curie-Weiss law. Heisenberg exchange

interaction. Mean field theory. Antiferromagnetism. Nel point. Nuclear magnetic resonance. Optical

Properties of Solids (6 L)

6. Energy bands in solids. The Bloch theorem. Bloch functions. Review of the Kronig-Penney model.

Brillouin zones. Number of states in the band. Band gap in the nearly free electron model. The tight

binding model. Electron dynamics in an electric field. The effective mass. Concept of hole. (7L)

7. Superconductivity, Survey of important experimental results. Critical temperature. Meissner effect.

Type I and type II superconductors. Thermodynamics of superconducting transition. London

equations. London penetration depth. Energy gap. Basic ideas of BCS theory. High-Tc

superconductors. (4L)

8. Tutorials. (5L)

Books recommended:

1. N. Ashcroft and N. Mermin: Solid State Physics (Holt, Reinhart and Winston). 2. M. Ali Omar: Elementary Solid State Physics (Pearson Education). 3. C. Kittel: Solid State Physics (Wiley Eastern). 4. F.C.Phillips: An introduction to crystallography (Wiley). 5. J. Christmaan: FundamentaL of Solid State Physics (John Wiley and Sons).

PAPER 302: Atomic and Molecular Spectroscopy

Atomic Spectroscopy:

1. Spectra of hydrogenic atoms. Fine structure; Relavistic correction. Spin-orbit interaction, Lamb shift. Spectra of alkali atoms. Quantum defect. Penetrating and non-penetrating orbits. Introduction to electron spin. Relativistic correction to spectra of hydrogen atom. The Lande g factor. Zeeman and Paschen- Back effects. Hyperfine structure in the spectra of monovalent atoms. (8L)

2. Spectra of divalent atoms. Singlet and triplet states of divalent atoms. L-S and j-j coupling. Magnetic field effects. Spectra of Many-electron atoms. Pauli exclusion principle. Periodic classification of elements. Equivalent and non-equivalent electrons. Spectral terms of equivalent and non-equivalent electrons for ground and first excited state electronic confugurations. (6L)

3. Origin of X-ray spectra. Screening constants. Fine structure of X-ray leveL. Spin-relativity and screening doublet laws. Non-diagram lines. Auger effect. (3L)

4. Broadening of spectral lines. Natural width of spectral lines, Doppler broadening. (2L) Molecular Spectroscopy:

5. Born-Oppenheimer approximation and separation of electronic and nuclear motions in molecules. Band structure of molecular spectra. Hydrogen molecule ion. Molecular orbitals. Hydrogen molecule. Valence bond approach. Coulomb and exchange integrals. Electronic structure of simple molecules. Chemical bonding. Hybridization. (4L)

6. Microwave and far infrared spectroscopy. Energy levels of diatomic molecules from rigid and nonrigid rotator models. Selection rules. Structure determination. Isotope effect. Rotational spectra of polyatomic molecules. (4L)

7. Infrared Spectra. Harmonic and anharmonic (no deduction) models for vibrational energy levels of diatomic molecules. Selection rules. Morse potential. Energy curves. Dissociation energy. Isotope effect. Rotational-vibrational coupling. Symmetry of molecular wavefunctions and nuclear spin. (4L)

8. Raman spectroscopy. Rotational, vibrational, Rotational-vibrational Raman spectra. Stokes and anti- Stokes Raman lines. Selection rules. Nuclear spin and its effect on Raman spectra. (3L)

9. Vibrational spectra of polyatomic molecules. Normal modes. Selection rules for Raman and infrared spectra. Normal modes of CO2 and other simple triatomic molecules. (3L)

10. Electronic spectra of diatomic molecules. Vibrational band structure. Progressions and sequences. Isotope shift. Intensity distribution in vibrational structure of electronic spectra. Franck-Condon principle. Rotational structure of electronic spectra. P-, Q-, and R- branches. Band head formation. Hund’s coupling cases. Pre-dissociation. Inversion spectrum of Ammonia. (3L)

11. Tutorials (5L).

Books Recommended:

1. H. White: Introduction to Atomic Spectra (McGraw-Hill). 2. B. Bransden and C. Joachain: Physics of Atoms and Molecules (Longman). 3. S. Ghoshal: Atomic and Nuclear Physics Vol I (S. Chand). 4. V. Jain: Introduction to Atomic and Molecular Spectroscopy (Narosa). 5. M. Weissbluth: Atoms and Molecules (Academic Press). 6. G. Herzberg: Molecular Spectroscopy (Diatomic Molecules) (Van Nostrand). 7. G. Barrow: Molecular Spectroscopy (McGraw-Hill). 8. J. Hollas: Modern Spectroscopy (John-Wiley and Sons). 9. C. Banwell and E. McCash: Fundamentals of Molecular Spectroscopy (TMH). 10. G. Aruldhas: Molecular Spectroscopy

PAPER 303: Plasma Physics

1. Elementary concepts of Plasma. Occurrence of plasma in nature, Concept of temperature, Concept of Debye shielding, plasma sheath, plasma oscillation, Plasma parameters, Plasma criteria. Applications of plasma physics. (3L)

2. Motion’ of charged particles in electromagnetic field. Uniform E and B fields, Non- uniform fields. Special variations of magnetic fields, gradient drift, parallel acceleration of guiding center. Magnetic mirror effect, Time-varying E and B fields. Adiabatic invariants (7L)

3. Hydrodynamical description of plasma. Fundamental fluid equations of Plasma, Fluid drift perpendicular to B, Fluid drift parallel to B. Plasma approximation. plasma oscillation. Effect of temperature. (3L)

4. Hydromagnetic equilibrium. Concept of . Diffusion of magnetic fields in plasma, Plasma instabilities. gravitational, two stream, Weibel instability. (4 L)

5. Diffusion and mobility in weakly ionized plasmas. Collision parameters. Ambipolar diffusion coefficient, Recombination. Plasma resistivity. (4L)

6. Plasma kinetic theory. Equation of kinetic theory, derivation of fluid equations. Plasma oscillations and Landau damping (qualitative discussion) and resonant particle. Experimental verification of Landau damping. (4L)

Books Recommended

1. Francis F. Chain: Introduction to Plasma Physics and Controlled Fusion. 2. J.A. Bittencourt: Fundamentals of Plasma physics 3. Ronald C. Davidson: Methods in Nonlinear Plasma Theory 4. Suresh Chandra : Textbook of Plasma Physics 5. Paul M bellan: Fundamentals of Plasma physics

PAPER 304: Optics Practical

List of Optics Experiments: 1. Study of absorption spectrum of Iodine vapor using optical spectrometer and determine its ( i)

Dissociation energy and (ii) Anharmonicity constant. 2. Determination of the thickness of a given transparent plate with the help of Jamins interferometer. 3. Determination of the refractive index of a given transparent thin film using Michelson interferometer. 4. Determination of the average wavelength and the difference between the wavelengths of the D– lines

of sodium using Michelson interferometer. 5. Study of Zeeman effect. 6. Study of Polarization of light using LASER beam. 7. Study of Photoconductivity of semiconductors. 8. Identification of hyperfine transitions of ଼ହ

ଷRb and ଼

ଷRb using saturation-absorption spectroscopy

method.

PAPER 305: Computer Practical

[A student needs to develop her/his own code for all the numerical methods learned and perform one (or two) program(s) during practical examination.]

1. Familiarity with LINUX and programming languages. Elements of Programming Language: Algorithms and flowchart. Structure of a high level language program. Constants and variables. Expressions. Input and output statements. Conditional statements and loop statements. Arrays. Functions.Structures. Pointer data type. List and trees.

2. Numerical techniques: Approximate numbers and Significant digits, Types of errors, General formula for errors, Order of errors.

3. Representation of integers and real numbers. Accuracy. Range. Overflow and underflow of number representation. Error propagation and instability. Solution of polynomial equations - bisection and Newton-Raphson algorithms. Interpolation- Lagrange’s interpolation formula. Least square fit. Matrix addition and multiplication. Numerical di_erentiation. Numerical integration trapezoidal formula, Simpsons formula.

Semester IV PAPER 401: Advanced Optics and Elective Paper

Unit-I Advanced Optics (25 Marks) 1. Coherence of light. Mutual coherence function. Complex degree of coherence. Quasi-monochromatic

fields and visibility. Spatial coherence of ordinary and laser light. Photon statistics. Poissonian photon statistics. Classification of light by photon statistics. Photon statistics of thermal and laser sources. Brown-Twiss correlations. Photon bunching and antibunching. (6L)

2. Historical background of laser. Einstein coefficients and stimulated light amplification. Gain and feedback. Threshold. Photon rate equations. Population rate equations. Population inversion. Creation of population inversion in three level and four level lasers. Small-signal gain and saturation. Pumping processes. (6L)

3. Basic Laser Systems. Gas Laser. CO2 laser. Solid State Laser: Host material and its characteristics. Doped ions. Nd:YAG laser. Liquid laser. Dye laser. Semiconductor laser. (3L)

4. Nonlinear Optics. Origin of nonlinearity. Nonlinear optical materials. Nonlinear polarization. Nonlinear susceptibilities. Self-focussing. Self-phase modulation. Second harmonic generation. Phase matching. Three-wave mixing. Parametric amplification and oscillation. (3L)

5. Fibre optics. Dielectric slab waveguide. Modes in the symmetric slab waveguide. TE and TM modes. Modes in the asymmetric slab waveguide. Coupling of the waveguide (edge, prism, grating). Dispersion and distortion in the slab waveguide. Integrated optics components (active, passive). Optical fibre waveguides (step index, graded index, single mode). Attenuation in fibre. Couplers and connectors. LED. Injection laser diode (double heterostructure, distributed feedback).(5L)

6. Detection of optical radiation. Photon detectors (photoconductive, photo voltaic detector and photoemissive detectors). p-i-n photodiode. APD photodiode.(2 L)

7. Tutorials. (3L)

Books recommended:

1. O. Svelto: Principles of lasers (Springer). 2. M. Fox: Quantum Optics (OUP) 3. P. Miloni and J. Eberly: Laser Physics (John Wiley). 4. A. Ghatak and K. Thyagarajan: Introduction to Fibre Optics. 5. D. Mills: Nonlinear Optics (Narosa).

Unit-II Elective Subject (25 Marks)

A. Astrophysics 1. Introduction: Astrophysics and Astronomy. Celestial coordinate systems (Sun-Earth system, Galactic

coordinate system). (2L) 2. Stellar Structure and Evolution: (i) Star formation. Stellar Magnitudes. Classification of stars. H-D

classification. Sahas equation of ionization. Hertzsprung-Russel (H-R) diagram. (ii) Gravitational energy, Virial theorem, Equations of stellar structure and evolution. (iii) Pre-main sequence evolution, Jeans criteria for star formation, fragmentation and adiabatic contraction, Evolution on the main sequence, Post main sequence evolution, Polytropic Models. Lane-Emden equation. Simple stellar models. Eddingtons model and Homologous model, Convective and Radiative stars, Pre-main sequence contraction: Hayashi and Henyey tracks. (8L)

3. Nuclear Astrophysics: Thermonuclear reactions in stars, pp chains and CNO cycle. Solar Neutrino problem. Thermonuclear reactions. Helium burning and onwards. Nucleosynthesis beyond iron, r- and s- processes. (3L)

4. Stellar objects and stellar explosions. Brief discussions on: Galaxies, Nebulae, Quasars, Brown dwarfs, Red giant stars, Nova, Supernova. (2L)

5. Gravitational collapse and relativistic astrophysics: Newtonian theory of stellar equilibrium. White dwarfs. Electron degeneracy and equation of states. Chandrasekhar limit. Mass-radius relation of WD. Neutron stars. Spherically symmetric distribution of perfect fluid in equilibrium. Tolman-Oppenheimer- Volko_ equation, Mass- radius relations of NS. Pulsars, Magnetars, Gamma ray bursts. Black holes: Collapse to a black hole (Oppenheimer and Snyder), event horizon, singularity. (7L)

6. Accretion disks: Formation of accretion disks. Di_erentially rotating systems in astrophysics. Disk dynamics. Steady disks. Disk formation in close binary systems through mass transfer. Accretion onto compact objects (Black holes and Neutron Stars). (3L)

Books Recommended: 1. V. Bhatia: Textbook of Astronomy and Astrophysics (Narosa). 2. K. Abhyankar: Astrophysics Stars and Galaxies (University Press).. 3. T. Padmanavan: Theoritical Astrophysics (VoL.I-III) (Cambridge University Press). 4. S. Shapiro and S. TeukoLky: Black Holes, White Dwarfs and Neutron Stars (John Wiley). 5. E. Kolb and M. Turner: The Early Universe (Addision-Wesley Reading). 6. J.V.Narlikar: The Structure of the Universe (Oxford University Press)

B. Advanced plasma physics:

1. Theory of plasma waves. Electron plasma waves, sound waves, Ion waves, Comparison of ion and electron wave. Electrostatic wave perpendicular to B and parallel to B , Electrostatic ion cyclotron wave, Electromagnetic wave perpendicular to B and parallel to B. Alfven wave. Derivation of dielectric tensor and dispersion relation for cold uniform magnetized plasma. Cut o_ and resonance. Mode conversion, acessibility condition, Ray Tracing, Whistlers, Warm plasma modes. Plasma heating method. ( 10 L)

2. Magnetohydrodynamic treatment of plasmas. Equilibrium equations, Approximations, magnetic surfaces, surface quantities, Relation among su_ace quantities, Flux co-ordinates, magnetic field representation. Gard-Shafranov (G-S) equation and examples of G-S solutions. Interchange, Sausage and Kink instabilities.( 10 L)

3. Nonlinear Phenomena: Large amplitude electron plasma oscillation, Exact solution in Lagrangian variable, extension of the model. Derivation Korteweg- de Vries equation for nonlinear sound wave. Solitary wave solution. Nonlinear drift-waves. (5 L)

Books Recommended: 1. Francis F. Chain: Introduction to Plasma Physics and Controlled Fusion. 2. J.A. Bittencourt: Fundamentals of Plasma physics 3. Ronald C. Davidson: Methods in Nonlinear Plasma Theory 4. Suresh Chandra : Textbook of Plasma Physics 5. Paul M bellan: Fundamentals of Plasma physics 6. S. Chandrasekhar: Plasma Physics.

C. General Relativity and Cosmology

1. Review of special theory of relativity: Poincare and Minkowskis 4-dimensional formulation. Geometrical representation of Lorentz transformations in Minkowskis space. Length contraction. Time dilation. Causality. Time-like and space-like vectors. Newtons second law of motion expressed in terms of 4-vectors. (4L)

2. Tensor calculus: Idea of Euclidean and non-Euclidean space. Meaning of parallel transport and covariant derivatives. Geodesics and autoparallel curves. Curvature tensor and its properties. Bianchi Identities. Vanishing of Riemann-Christo_el tensor as the necessary and su_cient condition of flatness. Ricci tensor. Einstein tensor. (5 L)

3. Einsteins field equations: Inconsistency of Newtonian gravitation with the special theory of relativity. Principles of equivalence. Principle of general covariance. Metric tensors and Newtonian Gravitational potential. Logical steps leading to Einsteins field equations of gravitation. Linearised equation for weak fields. Poissons equation. (4 L)

4. Applications of general relativity: Schwarzschilds exterior solution. Singularity. Event horizon and black holes. Isotropic coordinates. Birkho_s theorem. Observational tests of Einsteins theory. (4L)

5. Gravitational Collapse and Black Holes: Brief discussions on: White dwarfs, Neutron stars, static and rotating black holes (Schwarzschild and Reissner-Nordstrom). Kerr metric (derivation not required), event horizon, extraction of energy by Penrose process. Kerr-Neumann Metric (no derivation). No hair theorem. Cosmic censorship hypothesis. (3L)

6. Cosmology: Cosmological principles. Weyl postulates. Robertson-Walker metric (derivation is not required). Cosmological parameters. Static universe. Expanding universe. Open and closed universe. Cosmological red shift. Hubbles law. Olbers paradox. Brief discussions on: Big bang, Early universe (thermal history and nucleosynthesis), Cosmic microwave background radiation, Particle horizon. (5L)

Books Recommended:

1. J. Narlikar: General Relativity and Cosmology (MacMillion). 2. S. Weinberg: Gravitation and Cosmology: Principles and Applications of the General Theory of

Relativity (Wiley). 3. P. G. Bergmann- Introduction to Theory of Relativity (Prentice-Hall). 4. J. Narlikar: Introduction to Cosmology (Cambridge Univ. Press). 5. A. Roychaudhuri, S. Banerjee and A. Banerjee: General Relativity, Astrophysics and Cosmology

(Springer-Verlag). 6. S. Banerji and A. Banerjee: General Relativity and Cosmology (ELevier) 7. W. Rosser: Introduction to the Theory of Relativity

PAPER 402: Nuclear and Particle Physics

1. General properties of nuclei. Nuclear radius and charge distribution. Charge radius of nucleus from electron scattering experiment and the study of muonic x-rays. Charge form factor. Nuclear binding energy. Semi-empirical mass formulas. Angular momentum and parity of nuclei. Magnetic dipole moment. Electric quadrupole moment and nuclear shape. (6L)

2. Two-nucleon problem and nuclear forces. Ground and excited states of deuteron. Two-nucleon scattering. n-p scattering. Partial wave analysis. Phase-shift. Scattering length. Low energy p-p scattering (qualitative discussion). Charge symmetry and charge independence of nuclear forces. Isospin symmetry. Exchange interaction. Elementary discussion on Yukawas theory. (6L)

3. Nuclear modeL. Fermi gas model. Extreme single particle models. Spherical shell model. Collective model. (4 L)

4. Nuclear reactions. Conservation laws. Energetics. Q-value. Spontaneous fission. Mass and energy distribution of fragments. Direct and compound nuclear-reactions. Experimental verification of Bohrs independence hypothesis. Resonance reactions. Breit-Wigner dispersion relation. Stripping and pick up reactions (qualitative discussion only). Optical model. (5L)

5. Particle accelerators. Pelletron. Tandem principle. Synchrotron and synchrocyclotron. Colliding beams. Threshold energy for particle production. (4L)

6. Beta and Gamma decay. Fermis theory of beta decay. Allowed and forbidden transitions. Selection rules. Non-conservation of parity in beta decay. Detection of neutrino. Gammadecay and selection rules (derivation of transition probabilities not required). Internal conversion. (5L)

7. Energy loss of charged particles and gamma rays. Ionization formula, Stopping power and range. Radiation detectors. Multiwire proportional counter. Scintillation counter. Cerenkov detector. (5L)

8. Reactor Physics. Slowing down of neutrons in a moderator. Average log decrement of energy per collision. Slowing down power. Moderating ratio. Slowing down density. Fermi age equations. Fourfactor formula. Typical nuclear reactors. (5L)

9. High energy physics. Types of interaction in nature. Typical strengths and time-scales. Conservation laws. Charge-conjugation. Parity and Time reversal. CPT theorem, Gell-Mann-Nishijima formula. Intrinsic parity of pions. Quark model. Charm, beauty and truth. Gluons. Quark-confinement. Asymptotic freedom. Symmetry classification of elementary particles. Weak interactions-di_erent types. Selection rules. Parity violation and CP violation. (10L)

10. Tutorials. (5L) Books Recommended: 1. S. Ghoshal: Atomic and Nuclear Physics Vol II (S. Chand). 2. S. Wong: Introductory Nuclear Physics (PHI). 3. I. Kaplan: Nuclear Physics (Narosa). 4. K. Heyde: Basic Ideas and Concepts in Nuclear Physics (Institute of Physics Publishing). 5. B. Cohen: Concepts of Nuclear Physics (McGraw-Hill, India). 6. R. Roy and B. Nigam: Nuclear Physics (Wiley Eastern). 7. W. Meyerho_: Elements of Nuclear Physics (McGraw-Hill). 8. W. Burcham and M. Jobes: Nuclear and Particle Physics (Addison-Wesley). 9. A. Das and T. Ferbel: Introduction to Nuclear and Particle Physicss (World Scientific). 10. D. Perkins: Introduction to High Energy Physics (Addison-Wesley).

PAPER 403: Special Paper

A: Computational Physics 1. Mathematical Methods: Solution of simultaneous algebraic equations, Gauss elimination method,

pivoting. Eigenvalues and eigenvectors of a square matrix. Solution of ordinary differential equations, Euler method, Runge-Kutta methods (up to 4th order), finite difference method. Richardson’s extrapolation - Romberg’s integration. Monte-Carlo integration. Discrete and fast Fourier transforms. (13L)

2. Mechanics: Applications to simple mechanical problems, accelerated and circular motions, projectile. Planetary motion, Kepler’s laws. Oscillatory motion and waves, beats. (4L)

3. Quantum Mechanics: Solution of time-independent Schrodinger equation. Simple three point formula. Numerov’s method. Particle in infinite square well, harmonic oscillator, Gaussian wave packet. Perturbation applications, anharmonic oscillator. (5L)

4. ELectrodynamics: Potential and field due to point charge and simple charge distributions. Solution of Laplace’s and Poisson’s equations. Relaxation algorithm. Magnetic field produced by a current. Solenoid. (5L)

5. Random Systems: Use of random numbers. Monte-Carlo technique.Applications to Statistical Mechanics. Ising Model, Ferromagnetic to Paramagnetic phase transition. Metropolis algorithm. Random walk problem. Diffusion. (8L)

6. Non-linear Dynamics and Chaos: Phase plot and phase trajectories. Bifurcations- saddle node, pitch fork, transcritical Hopf bifurcations. Lorenz equation and study of chaos. Vander pol, Chua and other systems. Chaos in non-linear driven pendulum. Liyapunov exponent. Period doubling route to chaos, bifurcation plot, Poincare section. (8L)

7. Introduction to cellular automata and percolation. (2L) 8. Tutorials. (5L)

Books Recommended:

1. Nicholas Giordano and Hisao Nakanishi, Computational Physics, second edition, Prentice Hall (2005).

2. Paul L. DeVries and Javier E. Hasbun, A First Course in Computational Physics, 2nd ed., Jones and Bartlett (2010).

3. Harvey Gould, Jan Tobochnik, and Wolfgang Christian, Introduction to Computer Simulation Methods: Applications to Physical Systems, third edition, Addison-Wesley (2006).

4. Tao Pang, Computational Physics, second edition, Cambridge (2005). 5. David Potter, Computational Physics, John Wiley and Sons (1973). 6. William Gibbs, Computation in Modern Physics, World Scientific (2006), third edition. 7. K. Binder and D. W. Heerman, Monte Carlo Simulation in Statistical Physics, fifth edition, Springer-

Verlag (2010).

B: Advanced Electronics 1. Analog Circuits: Oscillators and voltage regulatores. Harmonic self-oscillators. Steady state operation

of self-oscillator. Nonlinear equation of self-oscillator. Op-amp based self-oscillator circuits. RC phase shift, LC,Wien bridge, Non-sinusoidal oscillators. Line and load regulation. Zener, op-amp, IC, Switching egulators. OP-AMP comparator. Multivibrator and timing circuits. IC 555 based timing circuits. (8 L)

2. Communication Principle: Review of CW Modulation Technique: Linear modulation DSB, SSB, VSB, QAM techniques, Exponential modulation FM and PM; AM and FM modulators and demodulators. Pulse and digital modulation tecnique. Principles of ASK, FSK, PSK, DPSK. Specialised Communication Systems: Basics of Satellite Communication. Orbits, Station keeping. Satellite attitude. Path loss calculation. Link calculation. Multiple access techniques. (10L)

3. Optoelectronics: Classification and fabrication principles of optical fibres. Wave propagation in optical fibre media. Losses in fibre. Optical fibre source and detector, Optical joints and Coupler, Fibre characteristics. Basic principles of optical fibre communication. Power budget equation; Multiplexing. Quantum limit. Signal-to-noise ratio calculation. (6L)

4. Antena and Radar System: Basic Considerations. antenna parameters. current distributions. Short electric doublet. half wave dipole. longer antenna. effect of ground; image antenna; Field strength at a point close to the antenna; microwave antenna and other direc- tional antennas. Basic pulsed radar system modulators, duplexer indicators, radar antenna CW radar. (5L)

5. Design of combinational and sequential circuits: registers, counters, gate arrays. Programmable logic devices PAL, GAL, PLA. Programmable gate arrays. (3 L)

6. Memories: Sequential and Random access memories. RAM bipolar and MOS static and dynamic memories. Programmable memories: PROM, EPROM, EEPROM. (3L)

7. Microprocessors and their applications. Architecture of 8 bit (8085) and 16 bit (8086) microprocessors. Addressing modes and assembly language programming of 8085 and 8086. Machine cycles and their timing diagrams. Interfacing concepts. Memory and I/O interfacing. Interrupts and interrupt controllers. Microprocessor based system design. (5 L)

Books recomended:

1. Geiger, Allen and Strader: VLI Design Techniques for Analog and Digital Circuits. 2. Gray and Meyer: Analysis and Design of Analog Integrated Circuits. 3. A Mathur: Microprocessors. 4. R. Gaonkar: Microprocessor Architecture, Programming and Applications with 8085/8085A (Second

Edition Penram International Publishing, India). 5. Lin and Gibson : Microprocessor (PHI). 6. S Soelof : Applications of Analog Integrated Circuits (PHI). 7. B. Brey: Intel Microprocessors Architecture, Programming and Interfacing (PHI). 8. A. Carlson: Communication Systems. 9. S. Haykin: Communication Systems (Wiley). 10. D. Roddy and J. Coolen: Electronic Communications. 11. Franz and Jain: Optical Communication Systems (Narosa). 12. A. Dhake: Television and Video Engineering (TMH). 13. Gulati: Monochrome and Color TV. 14. Kennedy and Davis; Electronic Communication Systems (TMH). 15. Taub and Schilling: Principle of Communication Systems (TMH). 16. B. P. Lathi: Modern Digital and Analog Communication Systems (Oxford).

PAPER 404: Special Practical

A: Computational Physics Students need to develop their own programs for all the problems studied and perform one (or two) program(s) during practical examination. B: Advanced Electronics Experiments

1. Experiments with OPAMP and timer IC Waveform generators square, triangular, sawtooth 2. Solution of simultaneous algebraic equations 3. Astable and monostable multivibrator with variable frequency and duty cycle using 555 IC. 4. Voltage controlled oscillator with 555 IC 5. Simple microprocessor programs, for example: (a) Average of some numbers (b) Testing even/odd

(c) Addition of 2 byte numbers (b) Multiplication of two 8 bit numbers (c) Division of two 8 bit numbers with (a) quotient only (b) both quotient and reminder (d) Testing for A = B, A > B and A < B conditions for two given numbers A and B (e) Sum of 10 even (odd) numbers (f) Factorial of a given number (g) To check the parity of a given number (h) To sort out the largest/smallest of a given set of numbers (i) To arrange a given set of numbers in ascending/descending order (j) Configuring delay programs for prescribed period (k) Display programs displaying in address field, data field and both

6. Characteristics of solar cell with variation in (i) waveband (ii) distance and (iii) area of exposure and calculation of parameters Optical communication with LED, photodiode and optical fibers

7. Experiments on digital electronics (a) Fabrication of shift register with JK master slave flip-flops and study of series and parallel in/out operations (b) Fabrication of counters of different modulus using JK master slave flip-flops. Use of 7490 counter chip (c) R2R ladder D/A converter (4 bit and 8 bit) (d) Use of 7483 adder chip as adder, subtractor and both (e) Diode ROM with decoder (f) Use of 7 segment display

8. Microprocessor Interfacing (a) Configure port A/port B/port C as output ports (b) Generate square waves (symmetric, asymmetric and variable amplitude) using 8255 IC and display in CRO (c) Generate triangular wave/saw tooth wave using 8255 IC and display in CRO (d) Control system, such as: (i) Stepper motor controller (ii) Use of relay module (e) Use of D/A and A/D converters (f) Introductory use of microcontroller

9. Experiments on microwave (a). Familiarity with microwave components and assembling those (b) Gunn diode characteristics (c) Use of waveguide and horn antenna in microwave communication.

PAPER 405: Project