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Ⅰ．INTRODUCTION 1

1．Description of experiments 1

2．The concept of physical system 3

3．Preparation and measurement 6

Ⅱ．STATES AND OBSERVABLES 10

1．States and amplitudes 10

2．An example:spin 1/2 14

3．Observables 20

4．The density operator 24

Ⅲ．COMMENSURABILITY 30

1．The spin example continued 30

2．Different kinds of measurement 32

3．Commensurable observables 34

4．The uncertainty relation 38

Ⅳ．DYNAMICS 40

1．The dynamical postulate 40

2．Schr？dinger, Heisenberg and mixed pictures 43

3．An aside on functions of several observables 47

4．The hamiltonian 50

5．Equations of motion in the different pictures 53

6．An example 58

Ⅴ．GENERAL FORMULATION 62

1．Generalization of the basic postulates 62

2．Dirac's formulation 65

3．Kinematical symmetries 68

4．The dynamics under a kinematical symmetry 69

5．The galilean transformations as kinematical symmetries 72

6．The generators of kinematical galilean transformations 78

7．Superselection rules 86

Ⅵ．A PARTICLE IN ONE DIMENSION 89

1．A particle without spin 89

2．The momentum operator 92

3．The velocity,the mass and the hamiltonian 94

4．An example:the harmonic oscillator 98

5．A particle in a constant force field 102

Ⅶ．A SPINLESS PARTICLE IN THREE DIMENSIONS 106

1．Position,momentum and the hamiltonian 106

2．Rotations,the orbital angular momentum 110

3．The angular momentum commutation relations 112

4．Spectral resolution of the orbital angular momentum 116

5．The free particle 119

6．The Wigner distribution function 121

7．The harmonic oscillator 123

8．The spinless particle in a general coordinate system 125

9．The particle in a central field 130

Ⅷ．DYNAMICAL SYMMETRIES AND CONSERVATION LAWS 133

1．The dynamical symmetry transformations of quantum mechanics 133

2．Unitary transformations and constants of the motion 135

3．Space inversion,the parity observable 139

4．Time reversal 142

5．The galilean transformations as dynamical symmetries 145

Ⅸ．A PARTICLE WITH SPIN 152

1．Internal degrees of freedom and galilean invariance 152

2．Spin and rotations 156

3．The particle with spin 160

4．The hamiltonian of a particle with spin 165

5．Example:a neutral particle in a magnetic field 171

Ⅹ．SYSTEMS COMPOSED OF DIFFERENT SUBSYSTEMS 175

1．The description of systems formed by different subsystems 176

2．A system of two different particles 177

3．Some useful representations 186

4．The state of a subsystem 190

5．Example:states of a particle in a magnetic field 195

Ⅺ．SYSTEMS OF IDENTICAL PARTICLES 202

1．The description of systems formed by two identical subsystems 202

2．Example:a system of two identical particles 209

3．The description of systems of many identical particles 213

4．Number representation of systems of identical particles 222

5．An assembly of bosons 223

6．An assembly of fermions 230

APPENDIX A.FINITE-DIMENSIONAL VECTOR SPACES 234

1．Basic definitions 234

2．Operators in unitary spaces 237

3．The spectral theorem 244

4．The tensor product 252

5．Antilinear operators 259

6．Wigner's theorem 260

APPENDIX B.THE HILBERT SPACE 264

1．Basic definitions,unbounded operators 264

2．The spectral theorem 267

3．Function space representation 278

APPENDIX C.DIRAC'S FORMULATION IN THE HILBERT SPACE 281

1．Tempered distributions 281

2．Generalization to an arbitrary Hilbert space 301

3．Dirac's formulation 303

APPENDIX D.A REMINDER FROM CLASSICAL MECHANICS 312

1．Canonical transformations 312

2．A reminder from classical mechanics 316

NOTES 320

BIBLIOGRAPHY 325

INDEX 328