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Practical quantum mechanics

Author: Siegfried Flügge
Publisher: Berlin ; New York : Springer, ©1999.
Series: Classics in mathematics.
Edition/Format:   Print book : EnglishView all editions and formats

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  Read more...


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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Siegfried Flügge
ISBN: 3540650350 9783540650355
OCLC Number: 39962044
Notes: "Reprint of the 1994 edition."
"Originally published as vol. 177 and 178 of the Grundlehren der mathematischen Wissenschaften"--Title page verso.
Includes index.
Description: xv, 287 pages : illustrations ; 24 cm.
Contents: I. General Concepts.- 1. Law of probability conservation.- 2. Variational principle of Schrodinger.- 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. Schrodinger 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. Poschl-Teller potential hole.- 39. Potential hole of modified Poschl-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 Schrodinger 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. Hulthen 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 Poschl-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 Schrodinger 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.
Series Title: Classics in mathematics.
Other Titles: Rechenmethoden der Quantentheorie.
Responsibility: Siegfried Flügge.
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