The Physics of Quantum Mechanics

《The Physics of Quantum Mechanics》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、ThePhysicsofQuantumMechanicsJamesBinneyandDavidSkinnerivCopyrightc2008–210JamesBinneyandDavidSkinnerPublishedbyCapellaArchive2008;revisedprintings2009,2010ContentsPrefacex1Probabilityandprobabilityamplitudes11.1Thelawsofprobability3•Expectationvalues41.2Probabilityampli

2、tudes5•Two-slitinterference6•Matterwaves?71.3Quantumstates7•Quantumamplitudesandmeasurements7⊲Completesetsofamplitudes8•Diracnotation8•Vectorspacesandtheiradjoints9•Theenergyrep-resentation11•Orientationofaspin-halfparticle12•Polarisationofphotons131.4Measurement15Probl

3、ems152Operators,measurementandtimeevolution172.1Operators17⊲Functionsofoperators20⊲Commutators202.2Evolutionintime21•Evolutionofexpectationvalues232.3Thepositionrepresentation24•Hamiltonianofaparticle26•Wavefunctionforwelldefinedmomentum27⊲Theuncertaintyprinciple28•Dynam

4、icsofafreeparticle29•Backtotwo-slitin-terference31•Generalisationtothreedimensions31⊲Probabilitycurrent32⊲Thevirialtheorem33Problems343Harmonicoscillatorsandmagneticfields373.1Stationarystatesofaharmonicoscillator373.2Dynamicsofoscillators41•Anharmonicoscillators423.3Mot

5、ioninamagneticfield45•Gaugetransformations46•LandauLevels47⊲Displacementofthegyrocentre49•Aharonov-Bohmef-fect51Problems524Transformations&Observables574.1Transformingkets57•Translatingkets58•ContinuoustransformationsviContentsandgenerators59•Therotationoperator61•Discre

6、tetransformations614.2Transformationsofoperators634.3Symmetriesandconservationlaws674.4TheHeisenbergpicture684.5Whatistheessenceofquantummechanics?70Problems715Motioninsteppotentials745.1Squarepotentialwell74•Limitingcases76⊲(a)Infinitelydeepwell76⊲(b)Infinitelynarrowwell

7、775.2Apairofsquarewells78•Ammonia80⊲Theammoniamaser815.3Scatteringoffreeparticles83⊲Thescatteringcrosssection85•Tunnellingthroughapotentialbarrier86•Scatteringbyaclassicallyallowedregion87•Resonantscattering89⊲TheBreit–Wignercrosssection915.4Howapplicableareourresults?9

8、45.5Whatwehavelearnt96Problems976Compositesystems1026.1Compositesystems103•Collapseofthewavefunction106•Operat