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Quantum mechanics of one and two-electron atoms / Hans A. Bethe, Edwin E. Salpeter
Titre : Quantum mechanics of one and two-electron atoms Type de document : texte imprimé Auteurs : Hans A. Bethe, Edwin E. Salpeter Editeur : Dover Publications Année de publication : 2008 Format : 24 cm ISBN/ISSN/EAN : 978-0-486-46667-5 Note générale : 978-0-486-46667-5 Langues : Anglais (eng) Catégories : Physique Mots-clés : Many:body problem
AtomsIndex. décimale : 530 Physique Résumé :
This classic of modern physics includes a vast array of approximation methods, mathematical tricks, and physical pictures that are also useful in the application of quantum mechanics to other fields. Students and professionals will find it an essential reference for calculations pertaining to hydrogen-like and helium-like atoms and their comparison with experimental results.
In-depth explorations of the Dirac theory of the electron and of radiative effects include brief accounts of relevant experiments. The specific application of general field-theoretic results to atomic systems also receives a thorough examination. Author Hans A. Bethe (1906–2005), Professor of Physics at Cornell University, won the Nobel Prize in Physics in 1967. Co-author Edwin E. Salpeter is James Gilbert White Distinguished Professor of the Physical Sciences at Cornell University.Note de contenu :
Sommaire
Introduction.
Units. 2
I.THE HYDROGEN ATOM WITHOUT EXTERNAL FIELDS 4
a) Nonrelativistic theory . . . . . . . . . . . . . . . . . 4
t. Separation of ScHRODINGER's equation in spherical polar coordinates.
Angularly dependent eigenfunctions and the angular momentum matrix 4
2. Derivation of BALMER's formula . . . . . . . . . 8
3. The radial eigenfunctions of the discrete spectrum 12
4. The eigenfunctions of the continuous spectrum . . 21
5. Motion of the nucleus . . . . . . . . . . . . . 25
6. Separation of ScHRODINGER's equation in parabolic coordinates . 27
7. Methods for the continuous spectrum for a general central potential . 32
8. Wave functions in momentum space. Discrete spectrum . . 36
9. Wave functions in momentum space. Continuous spectrum 40
b) DIRAC theory
to. 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
1 7. 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 SCHRODINGER 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
37. Motion of the nucleus
b) Relativistic theory . . . .
38. Discussion of the BREIT equation
39. The PAULI approximation (low Z)
VIII Contents.
40. Fine structure splitting of helium . . . . 183
41. Relativistic corrections for the ground state 189
42. BREIT equation without external field 192
43. Treatment for large Z . . . . . t96
44. Hyperfine structure . . . . . . 201
III. ATOMS IN EXTERNAL FIELDS . 205
a) ZEEMAN effect . . . . . . . . . 205
45. ZEEMAN effect for a single-electron atom . 205
46. Dependence on magnetic field strength 208
47. Some corrections to the ZEEMAN effect. 213
48. Extension to many-electron atoms. . . 218
49. Comparison with precision experiments 222
SO. The diamagnetism of helium 227
b) STARK effect in hydrogen 228
51. Linear STARK effect . . . 228
52. The quadratic STARK effect 232
53. STARK effect for strong fields . 234
54. Ionization by the electric field. Quenching of the lines in the STARK effect 235
55. STARK effect of the fine structure of hydrogen 238
c) STARK effect in helium 241
56. The STARK effect for weak fields 241
57. Dependence on field strength . . 244
58. The dielectric constant of helium 246
IV. INTERACTION WITH RADIATION 248
a) Discrete spectrum . . . . . . . . 248
59. General formulas . . . . . . . . 248
60. Selection rules for orbital and magnetic quantum numbers 252
6t. Sum rules . . . . . . . . . . . . . . . . . . . . . 255
62. Proof of the sum rules . . . . . . . . . . . . . . . . 259
63. The transition probabilities for hydrogen in polar coordinates . 262
64. Intensity of fine structure lines . . . . . . . . . 269
65. IHtensities in parabolic coordinates (STARK effect) . 276
66. Higher multipole radiation . . . . . . 278
67. Lifetimes of excited states in hydrogen 284
68. Alkali and X-ray spectra 292
b) The photoeffect . . . . . 295
69. General survey . . . . . 295
70. The BoRN approximation 299
71. The absorption coefficient without retardation 303
72. Angular distribution and retardation. 308
73. Relativistic effects. 311
74. The optical region 315
75. Recombination 320
c) Bremsstrahlung 323
76. General survey 323
77. Nonrelativistic BoRN approximation 326
78. Calculations for low energies . 331
79. Relativistic effects. . . . . . 336
Appendix on spherical harmonics 344
Bibliography 3 so
Addenda and errata 3 5 t
Author index . 360
Subject index . 365
Index of Tables 369Côte titre : Fs/14198 Quantum mechanics of one and two-electron atoms [texte imprimé] / Hans A. Bethe, Edwin E. Salpeter . - [S.l.] : Dover Publications, 2008 . - ; 24 cm.
ISBN : 978-0-486-46667-5
978-0-486-46667-5
Langues : Anglais (eng)
Catégories : Physique Mots-clés : Many:body problem
AtomsIndex. décimale : 530 Physique Résumé :
This classic of modern physics includes a vast array of approximation methods, mathematical tricks, and physical pictures that are also useful in the application of quantum mechanics to other fields. Students and professionals will find it an essential reference for calculations pertaining to hydrogen-like and helium-like atoms and their comparison with experimental results.
In-depth explorations of the Dirac theory of the electron and of radiative effects include brief accounts of relevant experiments. The specific application of general field-theoretic results to atomic systems also receives a thorough examination. Author Hans A. Bethe (1906–2005), Professor of Physics at Cornell University, won the Nobel Prize in Physics in 1967. Co-author Edwin E. Salpeter is James Gilbert White Distinguished Professor of the Physical Sciences at Cornell University.Note de contenu :
Sommaire
Introduction.
Units. 2
I.THE HYDROGEN ATOM WITHOUT EXTERNAL FIELDS 4
a) Nonrelativistic theory . . . . . . . . . . . . . . . . . 4
t. Separation of ScHRODINGER's equation in spherical polar coordinates.
Angularly dependent eigenfunctions and the angular momentum matrix 4
2. Derivation of BALMER's formula . . . . . . . . . 8
3. The radial eigenfunctions of the discrete spectrum 12
4. The eigenfunctions of the continuous spectrum . . 21
5. Motion of the nucleus . . . . . . . . . . . . . 25
6. Separation of ScHRODINGER's equation in parabolic coordinates . 27
7. Methods for the continuous spectrum for a general central potential . 32
8. Wave functions in momentum space. Discrete spectrum . . 36
9. Wave functions in momentum space. Continuous spectrum 40
b) DIRAC theory
to. 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
1 7. 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 SCHRODINGER 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
37. Motion of the nucleus
b) Relativistic theory . . . .
38. Discussion of the BREIT equation
39. The PAULI approximation (low Z)
VIII Contents.
40. Fine structure splitting of helium . . . . 183
41. Relativistic corrections for the ground state 189
42. BREIT equation without external field 192
43. Treatment for large Z . . . . . t96
44. Hyperfine structure . . . . . . 201
III. ATOMS IN EXTERNAL FIELDS . 205
a) ZEEMAN effect . . . . . . . . . 205
45. ZEEMAN effect for a single-electron atom . 205
46. Dependence on magnetic field strength 208
47. Some corrections to the ZEEMAN effect. 213
48. Extension to many-electron atoms. . . 218
49. Comparison with precision experiments 222
SO. The diamagnetism of helium 227
b) STARK effect in hydrogen 228
51. Linear STARK effect . . . 228
52. The quadratic STARK effect 232
53. STARK effect for strong fields . 234
54. Ionization by the electric field. Quenching of the lines in the STARK effect 235
55. STARK effect of the fine structure of hydrogen 238
c) STARK effect in helium 241
56. The STARK effect for weak fields 241
57. Dependence on field strength . . 244
58. The dielectric constant of helium 246
IV. INTERACTION WITH RADIATION 248
a) Discrete spectrum . . . . . . . . 248
59. General formulas . . . . . . . . 248
60. Selection rules for orbital and magnetic quantum numbers 252
6t. Sum rules . . . . . . . . . . . . . . . . . . . . . 255
62. Proof of the sum rules . . . . . . . . . . . . . . . . 259
63. The transition probabilities for hydrogen in polar coordinates . 262
64. Intensity of fine structure lines . . . . . . . . . 269
65. IHtensities in parabolic coordinates (STARK effect) . 276
66. Higher multipole radiation . . . . . . 278
67. Lifetimes of excited states in hydrogen 284
68. Alkali and X-ray spectra 292
b) The photoeffect . . . . . 295
69. General survey . . . . . 295
70. The BoRN approximation 299
71. The absorption coefficient without retardation 303
72. Angular distribution and retardation. 308
73. Relativistic effects. 311
74. The optical region 315
75. Recombination 320
c) Bremsstrahlung 323
76. General survey 323
77. Nonrelativistic BoRN approximation 326
78. Calculations for low energies . 331
79. Relativistic effects. . . . . . 336
Appendix on spherical harmonics 344
Bibliography 3 so
Addenda and errata 3 5 t
Author index . 360
Subject index . 365
Index of Tables 369Côte titre : Fs/14198 Exemplaires (1)
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