Quantum Mechanics and Quantum Mechanics and Atomic PhysicsAtomic Physics

Lecture 25:Lecture 25:Lecture 25:Lecture 25:

GRE problems and Review for FinalGRE problems and Review for Final

h // h i d / d/361h // h i d / d/361http://www.physics.rutgers.edu/ugrad/361http://www.physics.rutgers.edu/ugrad/361

Prof. Sean OhProf. Sean Oh

AnnouncementAnnouncementAnnouncementAnnouncementFinal Exam: Wed, December 21, 8:00Final Exam: Wed, December 21, 8:00--11:00 am, SEC11:00 am, SEC--209:209:209: 209:

Closed book with a Letter size formula sheet on both sidesClosed book with a Letter size formula sheet on both sidesThose who perform better in percentile score in the FinalThose who perform better in percentile score in the FinalThose who perform better in percentile score in the Final Those who perform better in percentile score in the Final exam compared to the Midterm will have their Midterm exam compared to the Midterm will have their Midterm percentile scores replaced by the final percentile percentile scores replaced by the final percentile scorescore..

Studying for the Physics GRE’sStudying for the Physics GRE’sStudying for the Physics GRE sStudying for the Physics GRE s

http://www.physics.rutgers.edu/~kalelkar/gre/Prohttp://www.physics.rutgers.edu/~kalelkar/gre/Prop p y g gp p y g gblems/Quantum/blems/Quantum/ is a collection of Quantum is a collection of Quantum questions from several practice GRE exams. questions from several practice GRE exams. h // h i d / k l lk / /Ph // h i d / k l lk / /Phttp://www.physics.rutgers.edu/~kalelkar/gre/Prohttp://www.physics.rutgers.edu/~kalelkar/gre/Problems/Atomic/blems/Atomic/ is a similar collection for Atomic is a similar collection for Atomic PhysicsPhysicsPhysicsPhysicshttp://grephysics.net/ans/http://grephysics.net/ans/ has solutions to the has solutions to the questionsquestions

Final exam preparationFinal exam preparationFinal exam preparationFinal exam preparation

In the order of highest priority:In the order of highest priority:In the order of highest priority:In the order of highest priority:Carefully review quizzes and midterm examCarefully review quizzes and midterm examG ll HW bl d lG ll HW bl d lGo over all HW problems and examples Go over all HW problems and examples discussed in lectures; pay special attention to discussed in lectures; pay special attention to h l /HW bl id R dh l /HW bl id R dthose examples/HW problems outside Reed those examples/HW problems outside Reed

book.book.Go through the entire lecture notes and make Go through the entire lecture notes and make sure that you UNDERSTAND all topicssure that you UNDERSTAND all topicsA number of problems will be GRE style!A number of problems will be GRE style!

TopicsTopicsTopicsTopics

De Broglie wavelengthDe Broglie wavelengthDe Broglie wavelengthDe Broglie wavelengthBohr’s Hydrogen modelBohr’s Hydrogen modelCl i l i QCl i l i QClassical wave equation vs. Quantum wave Classical wave equation vs. Quantum wave equationequationSolving infinite and finite potential wells: Solving infinite and finite potential wells: boundary boundary condictionscondictionsExpectation values: position, momentum, Expectation values: position, momentum, energy, angular momentum, etc.energy, angular momentum, etc.gy, g ,gy, g ,

TopicsTopicsTopicsTopics

Normalization andNormalization and OrthogonalityOrthogonalityNormalization and Normalization and OrthogonalityOrthogonalityWavefunctionWavefunction sketchsketchT lliT lli i i /Al h di i /Al h dTunnellingTunnelling: transmission/Alpha decay: transmission/Alpha decayUncertainty principle: how to use it.Uncertainty principle: how to use it.Meaning of commuting and nonMeaning of commuting and non--commuting commuting operatorsoperatorsppTime evolution of Time evolution of wavefunctionwavefunction: finding : finding ΨΨ(x, t) (x, t) out ofout of ΨΨ(x 0); see midterm(x 0); see midtermout of out of ΨΨ(x, 0); see midterm(x, 0); see midterm

TopicsTopicsTopicsTopics

How to useHow to use VirialVirial theorem: see midtermtheorem: see midtermHow to use How to use VirialVirial theorem: see midterm theorem: see midterm Harmonic oscillatorsHarmonic oscillatorsA lA lAngular momentumAngular momentumSpherical harmonicsSpherical harmonicsCentral Central vsvs nonnon--central potentialscentral potentialsSeparation of variablesSeparation of variablesSeparation of variables Separation of variables Radial solutions of central potentialsRadial solutions of central potentialsH dH d f if iHydrogen atom Hydrogen atom wavefunctionswavefunctionsSelection rules for Selection rules for radiativeradiative transitiontransition

TopicsTopicsTopicsTopics

LL22 LL SpinsSpinsLL , , LLzz, Spins, SpinsAngular momentum/spin additionAngular momentum/spin additionS iS i bi libi liSpinSpin--orbit couplingorbit couplingFine structure: Fine structure: ll and s combine into jand s combine into jOrigin of FineOrigin of Fine--structure splitting, Hyperstructure splitting, Hyper--fine fine splitting, Lamb shiftsplitting, Lamb shiftp g,p g,GyromagneticGyromagnetic ratio and g factor; magnetic ratio and g factor; magnetic momentmoment vsvs angular momentumangular momentummoment moment vsvs angular momentumangular momentumSplitting of energy levels in external BSplitting of energy levels in external B--fieldfield

TopicsTopicsTopicsTopicsIdentical particleIdentical particlePa li e cl sion principlePa li e cl sion principlePauli exclusion principlePauli exclusion principleSpin singlet vs. spin triplet effectSpin singlet vs. spin triplet effectSpatial vs total wave function symmetrySpatial vs total wave function symmetrySpatial vs. total wave function symmetry Spatial vs. total wave function symmetry FermionFermion vs. Bosonvs. BosonFilling electron shells/subFilling electron shells/sub--shells usingshells using Hund’sHund’s rulesrulesFilling electron shells/subFilling electron shells/sub shells using shells using Hund sHund s rules rules and Pauli exclusion principleand Pauli exclusion principleSpectroscopic notationSpectroscopic notationp pp pWKB methodWKB methodSuperposition theoremSuperposition theorem11stst order Perturbation theoryorder Perturbation theoryVariationalVariational methodmethod

Summary/AnnouncementsSummary/AnnouncementsSummary/AnnouncementsSummary/Announcements

Please fill out the course survey at: Please fill out the course survey at:

http://sakai.rutgers.eduhttp://sakai.rutgers.edu

Final Exam: Wed, December 21, 8:00Final Exam: Wed, December 21, 8:00--11:00 am, SEC11:00 am, SEC--209: 209: Closed book with a Letter size formula sheet on both sidesClosed book with a Letter size formula sheet on both sidesThose who perform better in percentile score in the Final exam Those who perform better in percentile score in the Final exam compared to the Midterm will have their Midterm percentile compared to the Midterm will have their Midterm percentile scores replaced by the final percentile score.scores replaced by the final percentile score.scores replaced by the final percentile score.scores replaced by the final percentile score.