Cohen--Lecture Notes in Quantum Mechanics .pdf

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1、LectureNotesinQuantumMechanicsDoronCohenDepartmentofPhysics,Ben-GurionUniversity,Beer-Sheva84105,IsraelThesearethelecturenotesofthequantummechanicscoursesthatweregivenbyDCatBen-GurionUniversityduring2005.Theycoverundergraduatetextbooktopics(e.g.asinSakurai),andalsoadditionaladvancedtop

2、icsatthesamelevelofpresentation.Thetopicsthatarecoveredare:Fundamentals:Dynamicsanddrivensystems•Theclassicaldescriptionofaparticle•Systemswithdriving•Hilbertspaceformalism•Theinteractionpicture•AparticleinanNsitesystem•Thetransitionprobabilityformula•Thecontinuumlimit(N=∞)•Fermigolden

3、rule•Translationsandrotations•CrosssectionsandBornformula•Thefundamentalpostulatesofthetheory•Theadiabaticequation•TheBerryphase•Theevolutionoperator•Theoryofadiabatictransport(*)•Therateofchangeformula•LinearresponsetheoryandKubo(*)•FindingtheHamiltonianforaphysicalsystem•TheBorn-Oppe

4、nheimerpicture(*)•Thenon-relativisticHamiltonian•The”classical”equationofmotionTheGreenfunctionapproach(*)•Symmetriesandconstantsofmotion•Theevolutionoperator•Grouptheory,Liealgebra•Feynmanpathintegral•Representationsoftherotationgroup•TheresolventandtheGreenfunction•Spin1/2,spin1andYℓ

5、,m•Multiplyingrepresentations•Perturbationtheoryfortheresolvent•Additionofangularmomentum(*)•Perturbationtheoryforthepropagator•TheGalileigroup(*)•Complexpolesfromperturbationtheory•Transformationsandinvariance(*)Scatteringtheory(*)Quantummechanicsinpractice:•Scattering:Tmatrixformalis

6、m•Thedynamicsofatwolevelsystem•Scattering:Smatrixformalism•FermionsandBosons•Scattering:Rmatrixformalism•Decayintothecontinuum•Cavitywithleads‘mesoscopic’geometry•TheAharonov-Bohmeffect•Sphericalgeometry,phaseshifts•Magneticfield(Landaulevels,Halleffect)•Crosssection,opticaltheorem,resona

7、nces•Thedynamicsofaparticlewithspin1/2•MotioninacentralpotentialSpecialTopics(*)•Implicationsofhaving”spin”onthedynamics•QuantizationoftheEMfieldApproximations:•Fockspaceformalism•Perturbationtheoryforeigenstates•TheWignerWeylformalism•Example:ringwithscattererandflux•Theoryofquantumme