From the reviews:“Anyone who has taught a course ofqnatum mechanics knows the difficulty of providing ptaehcalexamples which are within the mathematical competence of the students and can be completed in a reasonable time.In this book will be found 219 problems，together with their solutions,which will greatly extend the repertoire.(...) The first volume deals exclusively with one-body problems without spin.(...) In the second volume the problems cover a widerrange and include illustrations of the introduction of spin,the interactions between two and thee particles，quantum statisticsand the Dirac relativistic equation with shorter sections on non-stationary problems and radiation theory.(...)”(Nature.Sept 10,1971)“The student who can master these problems will have a good grasp of the practical applications of quantum theoy and，therefore，of the basic concepts as well.I recommendthe book un-reservedly.”
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目录
Ⅰ. General Concepts 1. Law of probability conservation 2. Variational principle of Schrödinger 3. Classical mechanics for space averages 4. Classical laws for angular motion 5. Energy conservation law 6. Hermitian conjugate 7. Construction of an hermitian operator 8. Derivatives of an operator 9. Time rate of an expectation value 10. Schrödinger and Heisenberg representations 11. Time dependent hamiltonian 12. Repeated measurement 13. Curvilinear coordinates 14. Momentum space wave functions 15. Momentum space: Periodic and aperiodic wave functions Ⅱ. One-Body Problems without Spin A. One-Dimensional Problems 16. Force-free case: Basic solutions 17. Force-free case: Wave packet 18. Standing wave 19. Opaque division wall 20. Opaque wall described by Dirac δ function 21. Scattering at a Dirac δ function wall 22. Scattering at a symmetric potential barrier 23. Reflection at a rectangular barrier 24. Inversion of reflection 25. Rectangular potential hole 26. Rectangular potential hole between two walls 27. Virtual levels 28. Periodic potential 29. Dirac comb 30. Harmonic oscillator 31. Oscillator in Hilbert space 32. Oscillator eigenfunctions constructed by Hilbert space operators 33. Harmonic oscillator in matrix notation 34. Momentum space wave functions of oscillator 35. Anharmonic oscillator 36. Approximate wave functions 37. Potential step 38. Pöschl-Teller potential hole 39. Potential hole of modified Pöschl-Teller type 40. Free fall of a body over earth's surface 41. Accelerating electrical field B. Problems of Two or Three Degrees of Freedom without Spherical Symmetry 42. Circular oscillator 43. Stark effect of a two-dimensional rotator 44. Ionized hydrogen molecule 45. Oblique incidence of a plane wave 46. Symmetrical top C. The Angular Momentum 47. Infinitesimal rotation 48. Components in polar coordinates 49. Angular momentum and Laplacian 50. Hilbert space transformations 51. Commutators in Schrödinger representation 52. Particles of spin 1 53. Commutation with a tensor 54. Quadrupole tensor. Spherical harmonics 55. Transformation of spherical harmonics 56. Construction of Hilbert space for an angular momentum component 57. Orthogonality of spherical harmonics D. Potentials of Spherical Symmetry a) Bound States 58. Angular momentum expectation values 59. Construction of radial momentum operator 60. Solutions neighbouring eigenfunctions 61. Quadrupole moment 62. Particle enclosed in a sphere 63. Square well of finite depth 64. Wood-Saxon potential 65. Spherical oscillator 66. Degeneracy of the spherical oscillator 67. Kepler problem 68. Hulth6n potential 69. Kratzer's molecular potential 70. Morse potential 71. Rotation correction of Morse formula 72. Yukawa potential hole 73. Isotope shift in x-rays 74. Muonic atom ground state 75. Central-force model of deuteron 76. Momentum space wave functions for central force potentials 77. Momentum space integral equation for central force potentials 78. Momentum space wave functions for hydrogen 79. Stark effect of a three-dimensional rotator b) Problems of Elastic Scattering 80. Interference of incident and scattered waves 81. Partial wave expansion of plane wave 82. Partial wave expansion of scattering amplitude 83. Scattering at low energies 84. Scattering by a constant repulsive potential 85. Anomalous scattering 86. Scattering resonances 87. Contribution of higher angular momenta 88. Shape-independent approximation 89. Rectangular hole: Low-energy scattering 90. Low-energy scattering and bound state 91. Deuteron potential with and without hard core 92. Low-energy cross section with and without hard core 93. Low-energy scattering by a modified Pöschl-Teller potential hole 94. Radial integral equation 95. Variational principle of Schwinger 96. Successive approximations to partial-wave phase shift 97. Calogero's equation 98. Linearization of Calogero's equation 99. Scattering length for a negative-power potential 100. Second approximation to Calogero equation 101. Square-well potential: Scattering length 102. Scattering length for a Yukawa potential 103. Improvement of convergence in a spherical harmonics series 104. Collision-parameter integral 105. Born scattering: Successive approximation steps 106. Scattering by a Yukawa potential 107. Scattering by an exponential potential 108. Born scattering by a charge distribution of spherical symmetry 109. Hard sphere: High energy scattering 110. Rutherford scattering formula 111. Partial wave expansion for the Coulomb field 112. Anomalous scattering 113. Sommerfeld-Watson transform 114. Regge pole E. The Wentzel-Kramers-Brillouin (WKB) Approximation 115. Eikonal expansion 116. Radial WKB solutions 117. WKB boundary condition of Langer 118. Oscillator according to WKB approach 119. WKB eigenvalues in a homogeneous field 120. Kepler problem in WKB approach 121. WKB phases in the force-free case 122. Calculation of WKB phases 123. Coulomb phases by WKB method 124. Quasipotential F. The Magnetic Field 125. Introduction of a magnetic field 126. Current in presence of a magnetic field 127. Normal Zeeman effect 128. Paramagnetic and diamagnetic susceptibilities without spin Ⅲ. Particles with Spin A. One-Body Problems 129. Construction of Pauli matrices 130. Eigenstates of Pauli matrices 131. Spin algebra 132. Spinor transformation properties 133. Spin electron in a central field 134. Quadrupole moment of a spin state 135. Expectation values of magnetic moments 136. Fine structure 137. Plane wave of spin 1/2 particles 138. Free electron spin resonance B. Two- and Three-Body Problems 139. Spin functions for two particles 140. Spin-dependent central force between nucleons 141. Powers of spin operators 142. Angular momentum eigenfunctions of two spin particles 143. Tensor force operator 144. Deuteron with tensor interaction 145. Electrical quadrupole and magnetic dipole moments of deuteron 146. Spin functions of three particles 147. Neutron scattering by molecular hydrogen Ⅳ. Many-Body Problems A. Few Particles 148. Two repulsive particles on a circle 149. Three-atomic linear molecule 150. Centre-of-mass motion 151. Virial theorem 152. Slater determinant 153. Exchange in interaction terms with Slater determinant 154. Two electrons in the atomic ground state 155. Excited states of the helium atom 156. Excited S states of the helium atom 157. Lithium ground state 158. Exchange correction to lithium ground state 159. Dielectric susceptibility 160. Diamagnetic susceptibility of neon 161. Van der Waals attraction 162. Excitation degeneracy 163. Neutral hydrogen molecule 164. Scattering of equal particles 165. Anomalous proton-proton scattering 166. Inelastic scattering B. Very Many Particles: Quantum Statistics 167. Electron gas in a metal 168. Paramagnetic susceptibility of a metal 169. Field emission, uncorrected for image force 170. Field emission, corrected for image force 171. White dwarf 172. Thomas-Fermi approximation 173. Amaldi correction for a neutral atom 174. Energy of a Thomas-Fermi atom 175. Virial theorem for the Thomas-Fermi atom 176. Tietz approximation of a Thomas-Fermi field 177. Variational approximation of Thomas-Fermi field 178. Screening of K electrons Ⅴ. Non-Stationary Problems 179. Two-level system with time-independent perturbation 180. Periodic perturbation of two-level system 181. Dirac perturbation method 182. Periodic perturbation: Resonance 183. Golden Rule for scattering 184. Born scattering in momentum space 185. Coulomb excitation of an atom 186. Photoeffect 187. Dispersion of light. Oscillator strengths 188. Spin flip in a magnetic resonance device Ⅵ. The Relativistic Dirac Equation 189. Iteration of the Dirac equation 190. Plane Dirac waves of positive energy 191. Transformation properties of a spinor 192. Lorentz covariants 193. Parity transformation 194. Charge conjugation 195. Mixed helicity states 196. Spin expectation value 197. Algebraic properties of a Dirac wave spinor 198. Current in algebraic formulation 199. Conduction current and polarization current 200. Splitting up of Dirac equations into two pairs 201. Central forces in Dirac theory 202. Kepler problem in Dirac theory 203. Hydrogen atom fine structure 204. Radial Kepler solutions at positive kinetic energies 205. Angular momentum expansion of plane Dirac wave 206. Scattering by a central force potential 207. Continuous potential step 208. Plane wave at a potential jump 209. Reflected intensity at a potential jump Ⅶ. Radiation Theory 210. Quantization of Schrödinger field 211. Scattering in Born approximation 212. Quantization of classical radiation field 213. Emission probability of a photon 214. Angular distribution of radiation 215. Transition probability 216. Selection rules for dipole radiation 217. Intensities of Lyman lines 218. Compton effect 219. Bremsstrahlung Mathematical Appendix Coordinate systems ґ function Bessel functions Legendre functions Spherical harmonics The hypergeometric series The confluent series Some functions defined by integrals Index for Volumes Ⅰ and Ⅱ
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