Quantum mechanics of one-and two-electron atoms / Hans A. Bethe and Edwin E. Salpeter

"A Plenum/Rosetta edition."

Units.- I. The Hydrogen Atom Without External Fields.- a) Nonrelativistic theory.- 1. Separation of Schrödinger’s equation in spherical polar coordinates. Angularly dependent eigenfunctions and the angular momentum matrix.- 2. Derivation of Balmer’s formula.- 3. The radial eigenfunctions of the discrete spectrum.- 4. The eigenfunctions of the continuous spectrum.- 5. Motion of the nucleus.- 6. Separation of Schrödinger’s equation in parabolic coordinates.- 7. Methods for the continuous spectrum for a general central potential.- 8. Wave functions in momentum space. Discrete spectrum.- 9. Wave functions in momentum space. Continuous spectrum.- b) Dirac theory.- 10. General properties of the Dirac theory.- 11. Angular momentum.- 12. Pauli theory of the spin-electron.- 13. Pauli theory for a central potential.- 14. The exact solution of the Dirac equation.- 15. Dirac equation. Continuous spectrum.- 16. The Dirac equation in momentum space.- 17. The fine structure formula.- c) Radiative and other corrections.- 18. Radiative corrections. S-matrix theory.- 19. Radiative corrections. Bound states.- 20. Corrections for nuclear motion and structure.- 21. Fine structure and the Lamb shift.- 22. Hyperfine structure splitting.- 23. The fine structure of positronium.- II. The Helium Atom without External Fields.- a) Nonrelativistic theory.- 24. The Schrödinger equation for helium (symmetry).- 25. Discussion of variation and perturbation methods.- 26. Level scheme of helium.- 27. Survey of approximations to be used.- 28. First order Heisenberg’s method (excited states).- 29. Polarization for excited states.- 30. Fock’s method (excited S-states).- 31. Hartree’s method.- 32. Ritz variation method (helium ground state).- 33. Ground state of helium-like ions with arbitrary Z.- 34. The negative hydrogen ion.- 35. Variation method for excited states.- 36. Miscellaneous calculations I.- 37. Motion of the nucleus.- b) Relativistic theory.- 38. Discussion of the Breit equation.- 39. The Pauli approximation (low Z).- 40. Fine structure splitting of helium.- 41. Relativistc corrections for the ground state.- 42. Breit equation without external field.- 43. Treatment for large Z.- 44. Hyperfine structure.- III. Atoms in External Fields.- a) Zeeman effect.- 45. Zeeman effect for a single-electron atom.- 46. Dependence on magnetic field strength.- 47. Some corrections to the Zeeman effect.- 48. Extension to many-electron atoms.- 49. Comparison with precision experiments.- 50. The diamagnetism of helium.- b) Stark effect in hydrogen.- 51. Linear Stark effect.- 52. The quadratic Stark effect.- 53. Stark effect for strong fields.- 54. Ionization by the electric field. Quenching of the lines in the Stark effect.- 55. Stark effect of the fine structure of hydrogen.- c) Stark effect in helium.- 56. The Stark effect for weak fields.- 57. Dependence on field strength.- 58. The dielectric constant of helium.- IV. Interaction with Radiation.- a) Discrete spectrum.- 59. General formulas.- 60. Selection rules for orbital and magnetic quantum numbers.- 61. Sum rules.- 62. Proof of the sum rules.- 63. The transition probabilities for hydrogen in polar coordinates.- 64. Intensity of fine structure lines.- 65. Intensities in parabolic coordinates (Stark effect).- 66. Higher multipole radiation.- 67. Lifetimes of excited states in hydrogen.- 68. Alkali and X-ray spectra.- b) The photoeffect.- 69. General survey.- 70. The Born approximation.- 71. The absorption coefficient without retardation.- 72. Angular distribution and retardation.- 73. Relativistic effects.- 74. The optical region.- 75. Recombination.- c) Bremsstrahlung.- 76. General survey.- 77. Nonrelativistic Born approximation.- 78. Calculations for low energies.- 79. Relativistic effects.- Appendix on spherical harmonics.- Addenda and errata.- Further addenda and errata.- Author index.- Index of Tables.