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Ⅰ．Brief review of historical development1

1. Black body radiation1

2. Photoelectric effect2

3. Specific heat of solids3

4. Compton effect4

Problems4

Ⅱ．Uncertainty and complementarily6

1. Einstein relations and Bohr complimentarity principle6

2. Wave-particle duality and quantum behavior9

3. De Broglie relation and Heisenberg uncertainty relation10

4. Further remarks on the uncertainty principle11

Problems14

Ⅲ．The Schr？dinger wave equation15

1. Postulates of quantum mechanics15

2. The Schr？dinger equation for free particles15

3. Probability distributions17

4. Operators and expectation values20

5. Motion of a free wave packet21

6. Schr？dinger equation for a particle in external fields23

7. Schr？dinger equation for a system of interacting particles25

Problems28

Ⅳ．Heisenberg equation of motion and commutators31

1. Heisenberg equation of motion31

2. Commutation relations33

Problems36

Ⅴ．Symmetry properties and conservation laws38

1. Uniformity of time38

2. Uniformity of space39

3. Isotropy of space40

4. Discrete transformation42

5. Reduction of the two-body problem43

Problems44

Ⅵ．Eigenfunctions and eigenvalues46

1. Stationary states46

2. Spectrum of the Hamiltonian48

3. Dirac's δ-function49

4. Orthonormality and completeness52

5. Density of states56

6. Linear vector space58

7. Simultaneous eigenfunctions and compatible observables59

8. Probability amplitudes62

Problems64

Ⅶ．The classical limit and WKB method66

1. Ehrenfest theorem66

2. Classical limit of Schr？dinger equation69

3. The semi-classical approximation for stationary states70

4. The quantization rule of Bohr and Sommerfield74

Problems77

Ⅷ．Illustrative examples in one dimension78

1. Square well potential78

2. Scattering from the square well—resonances and virtual states80

3. Periodic potential—Kronig-Penney model83

4. The δ function potential85

5. Linear harmonic oscillator88

Problems92

Ⅸ．Illustrative examples in three dimensional space95

1. The wave equation in spherical coordinates95

2. Symmetry properties of the central field problem97

3. Angular momentum eigenstates98

4. Free particle motion with a definite l101

5. Isotropic square well104

6. Hydrogen atom106

7. Degeneracy of hydrogen energy levels108

8. Electron in magnetic fields—a cylindrical field problem111

9. Examples in the confined and low-dimensional space112

Problems118

Ⅹ．Angular momentum122

1. Matrix representation of angular momentum operators122

2. Spin eigenvectors124

3. Coupling of two angular momentum vectors125

4. Rotation matrices130

5. Arbitrary rotation of a rigid body133

Problems135

Ⅺ．Unitary transformation138

1. States and operators138

2. Unitary operators and unitary transformations141

3. Observables in different representations143

4. Schr？dinger,Heisenberg and interaction pictures146

5. The interaction picture148

6. Pure and mixed states150

Problems157

Ⅻ．Approximation methods158

1. Variation method158

2. Perturbation theory for non-degenerate stationary states162

3. Validity of the perturbation method166

4. Perturbation theory for degenerate states167

5. Fine structure of hydrogen atomic spectra168

6. Atoms in external magnetic fields172

Problems177

ⅩⅢ．Many-electron systems180

1. Indistinguishability and Pauli principle180

2. Symmetrization and anti-symmetrization of wave functions182

3．Ground state of helium atom186

4．Excited states of helium atom189

5．Slater determinant for many-electron atoms192

6．Hartree-Fock method194

7．Statistical model of Fermi-Thomas198

Problems201

ⅩⅣ．Theory of time-dependent perturbation203

1．Time-dependent perturbation203

2．Transition probability per unit time206

3．Adiabatic and sudden approximation208

4．Induced emission,absorption and spontaneous emission209

5．Multipole radiation and selection rules214

6．Lifetime and width of excited levels216

7．Photoelectric effect219

8．Magnetic resonance223

9．Oscillating strength229

Problems230

ⅩⅤ．Theory of scattering233

1．General theory of elastic scattering233

2．Green function for a free particle235

3．The Born approximation238

4．Validity criteria for the Born approximation240

5．Method of partial waves241

6．Eikonal approximation247

7．Elastic scattering from the Coulomb potential249

8．General theory of inelastic scattering—The Lipman-Schwingwer formulation251

9．Scattering from complex targets255

Problems257

References260

Index262