Riassunto
This work was first published in 1947 in German under the title "Re- chenmethoden der Quantentheorie". It was meant to serve a double purpose: to help both, the student when first confronted with quantum mechanics and the experimental scientist, who has never before used it as a tool, to learn how to apply the general theory to practical problems of atomic physics. Since that early date, many excellent books have been written introducing into the general framework of the theory and thus indispensable to a deeper understanding. It seems, however, that the more practical side has been somewhat neglected, except, of course, for the flood of special monographs going into broad detail on rather restricted topics. In other words, an all-round introduction to the practical use of quantum mechanics seems, so far, not to exist and may still be helpful. It was in the hope of filling this gap that the author has fallen in with the publishers' wish to bring the earlier German editions up to date and to make the work more useful to the worldwide community of science students and scientists by writing the new edition in English. From the beginning there could be no doubt that the work had to be much enlarged. New approximation methods and other developments, especially in the field of scattering, had to be added. It seemed necessary to include relativistic quantum mechanics and to offer, at least, a glimpse of radiation theory as an example of wave field quantization.
Contenuti
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 ? function.- 21. Scattering at a Dirac ? 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. Diraccomb.- 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. Particlcs 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. Hulthén 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 quadrupolc 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 Append.- Coordinate systems.- ? function.- Bessel functions.- Legendre functions.- Spherical harmonics.- The hypergeometric series.- The confluent scries.- Some functions defined by integrals.- Index for Volumes I and II.
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