Quantum Mechanics.pdf

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1、QuantumMechanics2ndterm2002MartinPlenioImperialCollegeVersionJanuary28,2002Officehours:Tuesdays11am-12noonand5pm-6pm!Office:Blackett622Availableat:ContentsIQuantumMechanics51MathematicalFoundations111.1Thequantummechanicalstatespace...........111.2Thequantummechanicalst

2、atespace...........121.2.1FromPolarizedLighttoQuantumTheory....121.2.2Complexvectorspaces...............201.2.3BasisandDimension................231.2.4ScalarproductsandNormsonVectorSpaces...261.2.5CompletenessandHilbertspaces.........361.2.6Diracnotation............

3、........391.3LinearOperators......................401.3.1DefinitioninDiracnotation............411.3.2AdjointandHermiteanOperators.........431.3.3Eigenvectors,EigenvaluesandtheSpectralThe-orem.........................451.3.4FunctionsofOperators...............511.4Oper

4、atorswithcontinuousspectrum...........571.4.1Thepositionoperator...............571.4.2Themomentumoperator..............611.4.3Thepositionrepresentationofthemomentumoperatorandthecommutatorbetweenpositionandmomentum...................622QuantumMeasurements652.1Thepro

5、jectionpostulate..................652.2Expectationvalueandvariance...............702.3UncertaintyRelations....................7112CONTENTS2.3.1Thetraceofanoperator..............742.4Thedensityoperator....................762.5Mixedstates,Entanglementandthespeedofligh

6、t....822.5.1Quantummechanicsformanyparticles......822.5.2Howtodescribeasubsystemofsomelargesystem?862.5.3Thespeedoflightandmixedstates........902.6Generalizedmeasurements.................923DynamicsandSymmetries933.1TheSchr¨odingerEquation.................933.1.1The

7、Heisenbergpicture...............963.2SymmetriesandConservationLaws............983.2.1Theconceptofsymmetry.............983.2.2TranslationSymmetryandmomentumconserva-tion.........................1033.2.3RotationSymmetryandangularmomentumcon-servation..................

8、....1053.3Generalpropertiesofangularmomenta..........1083.3.1Rotations......................1083.3.2Grouprepresentationsandangularmomentum