Guided Study: A Quick Run Through Classical

and Quantum MechanicsMsc Student: Alan Leung Shek Lun

Advisor: Professor Hui Pak Ming

OutlineClassical Mechanics (mass-spring system)

1. Newton’s laws of motion2. Momentum3. Work-energy Theorem4. Potential Energy and force

(relation)5. Harmonic Oscillator6. Lagrangian Mechanics and

Hamiltonian Mechanics

Quantum Mechanics1. Schrodinger Equation2. Typical 1D problems3. Typical 2D and 3D problems

and their key features4. Quantum Harmonic Oscillator

Classical Mechanicsmass-spring system

Newton’s law of motion

Newton's law of motion

Newton’s law of motion

Relation of Force and Potential Energy

Work and Energy Theorem

Total Mechanical Energy

Conservation of Energy

Boundary Condition

Phase Diagram of momentum and position

Lagrangian Mechanics

Euler-Lagrange Equation

Conservative law

Conservative law

Hamiltonian Mechanics

Conservation of Energy

Total Mechanical Energy

5 postulates in Quantum Mechanics

Quantum MechanicsSchrodinger Equation

For harmonic oscillator, it can be expressed as

Quantum MechanicsTypical 1D problem

A free particle

Particle in an infinite well

Finite Potential Well (bound states)

Simulation

The one dimensi onal particle in a Box

Simulation

Superposition States in an infinite square well

Quantum Mechanics2D and 3D problems and their key features

Simulation

Energy Eigenfunction of the two dimensional infinite well

Quantum MechanicsHarmonic Oscillator

Ladder Operator Method

Quantum Harmonic Oscillator Energy level