Notes on Quantum Mechanics

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1、NotesonQuantumMechanicsFinnRavndalInstituteofPhysicsUniversityofOslo,Norwaye-mail:finnr@fys.uio.nov.4:December,20062Contents1Linearvectorspaces71.1Realvectorspaces...............................71.2Rotations...................................91.3Liegroups...................................111

2、.4Changeofbasis................................121.5Complexvectorspaces............................121.6Unitarytransformations...........................142Basicquantummechanics172.1Braandketvectors..............................172.2OperatorsinHilbertspace..........................192.3Matrix

3、representations............................202.4Adjointoperations..............................212.5Eigenvectorsandeigenvalues.........................222.6Thequantumpostulates...........................232.7Ehrenfest’stheorem..............................252.8Thetimeevolutionoperator........

4、.................252.9Stationarystatesandenergybasis......................272.10Changeofbasis................................282.11Schr¨odingerandHeisenbergpictures....................292.12TheLieformula................................312.13WeylandCambell-Baker-Hausdorffformulas...............

5、.323Discretequantumsystems353.1Matrixmechanics...............................353.2Thehydrogenmolecule............................3634CONTENTS3.3Thegeneraltwo-statesystem........................383.4Neutrinooscillations.............................403.5Reflectioninvarianceandsymmetrytransformat

6、ions............413.6Latticetranslationinvariance........................433.7Latticedynamicsandenergybands.....................453.8Three-dimensionallattices..........................474Schr¨odingerwavemechanics514.1Coordinatebasis...............................514.2TheDiracδ-function.......

7、......................524.3Continuoustranslationsandmomentum..................534.4Operatorsinthecoordinaterepresentation.................554.5Themomentumrepresentation........................584.6Threedimensions..............................