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Large order perturbation theory and summation methods in quantum mechanics /
Large order perturbation theory and summation methods in quantum mechanics

Author: G.A. Arteca, F.M. Fern�andez, E.A. Castro. Fern�andez, F. M. ; G A Arteca; F M Fernández; E A Castro
Publisher: Berlin ; New York : Springer-Verlag, ©1990.
Series: Lecture notes in chemistry, 53.
Edition/Format:   Print book : EnglishView all editions and formats
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The book provides a general, broad approach to aspects of perturbation theory. The aim has been to cover all topics of interest, from construction, analysis, and summation of perturbation series to  Read more...

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Additional Physical Format: Online version:
Arteca, G.A. (Gustavo Alberto).
Large order perturbation theory and summation methods in quantum mechanics.
Berlin ; New York : Springer-Verlag, ©1990
(OCoLC)625590609
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: G.A. Arteca, F.M. Fern�andez, E.A. Castro. Fern�andez, F. M. ; G A Arteca; F M Fernández; E A Castro
ISBN: 3540528474 9783540528470 0387528474 9780387528472
OCLC Number: 21975294
Description: xi, 644 pages : illustrations ; 25 cm.
Contents: A.- I. General Properties of the Eigenvalue Spectrum.- 1. Some Fundamental Properties.- 2. The Hellmann-Feynman Theorem.- 3. Hypervirial Relations and General Boundary Conditions.- References Chapter I.- II. The Semiclassical Approximation and the JWKB Method.- 4. Adiabatic Invariants.- 5. Bohr-Sommerfeld Quantization Condition and JWKB Method.- 6. Applications of the JWKB Method.- References Chapter II.- III. Rayleigh-Schroedinger Perturbation Theory (RSPT).- 7. The Rayleigh-Schroedinger Perturbation Theory.- 8. Hypervirial Method to Generate the Perturbation Expansion.- 9. Other Methods to Generate the Perturbation Expansion.- References Chapter III.- IV. Divergence of the Perturbation Series.- 10. Divergence of the perturbation series.- 11. Mathematical Methods to study the Asymptotic Behaviour of the RS coefficients.- References of Chapter IV.- V. Perturbation Series Summation Techniques.- 12. Introduction to the summability of divergent or slowly convergent series.- 13. Pade Approximants.- 14. Borel transform and Borel-Pade summation method.- 15. Euler Summation Method.- 16. Perturbation series renormalization techniques.- 17. Wick ordering and perturbation series summation.- 18. Summation of perturbation series through orderdependent mappings.- References Chapter V.- VI. Foundations of the Variational Functional Method (VFM).- 19. Energy of parameter-dependent systems.- 20. Semiclassical functional expressions for the energy.- 21. Scaling Variational Method.- 22. VFM from Heisenberg inequalities.- References Chapter VI.- VII. Application of the VFM to One-Dimensional Systems with Trivial Boundary Conditions.- 23. Anharmonic oscillators and variational functional: general properties.- 24. Translation of Coordinates and Variational Functional.- 25. Central Field Systems.- 26. Application of the variational functional to systems with confining potential.- References Chapter VII.- VIII Application of the VFM to One-Dimensional Systems with Boundary Conditions for Finite Values of the Coordinates.- 28. Functionals for Systems with Dirichlet Boundary conditions.- 29. Bounded harmonic oscillator: Approximation of its eigenvalues with the VFM.- References Chapter VIII.- IX Multidimensional Systems: The Problem of the Zeeman Effect in Hydrogen.- 30. Importance of the problem and applications of the model.- 31. Application of non-perturbative methods.- 32. Application of perturbation methods.- References Chapter IX.- X Application of the VFM to the Zeeman Effect in Hydrogen.- 33. Derivation of the variational functional.- 34. Results for several functions of physical interest.- 35. Scaling laws and semiclassical behavior of the Variational functional.- References Chapter X.- XI Combination of VFM with RSPT: Application to Anharmonic Oscillators.- 36. An elementary extension of the VFM for anharmonic oscillators.- 37. Application of the VFM to the theory of anharmonicity regimes.- 33. Another extension of the VFM for anharmonic oscillators.- References Chapter XI.- XII Geometrical Connection between the VFM and the JWKB Method.- 39. VFM and JWCB integrals for 1D systems with even potentials.- 40. VFM and JWKB integrals for 1D systems with potentials without defined parity and central field systems.- 41. Generalization of geometrical relations and RSPT.- References Chapter XII.- B.- XIII Generalization of the Functional Method as a Summation Technique of Perturbation Series.- 42. Generalization of the FM: Connection between semiclassical relations and renormalized series.- 43. Connection between the Fri and other summation techniques.- 44. Formulation of the FM from scaling laws (dilatation relationships).- References Chapter XIII 33.- XIV Properties of the FM: Series with Non-Zero Convergence Radii.- 45. Simple eigenvalue problems with branch-point singularities.- 46. Numerical Results for Simple Examples.- 47. Geometrical Series and FM.- 48. Further comments on series with non-zero con-vergence radii.- References Chapter XIV.- XV Properties of the FM: Series with Zero Convergence Radii.- 49. FM and asymptotic properties of Taylor coefficients of a series with zero convergence radius.- 50. Application of the FM to integrals of interest in field theory and statistical mechanics.- 51. Convergence conditions for the FM: Discussion of integrals with factorial divergence.- References Chapter XV.- XVI Appication of the FM to the Anharmonic Oscillator.- 52. Renormalization of the RS perturbation series with the FM: convergence to the ground state of the purely quartic oscillator.- 53. Further results for the eigenvalues of quartic anharmonic oscillators.- References Chapter XVI.- XVII Application of the FM to Models with Confining Potentials.- 54. Convergence of renormalized series in the strong coupling limit.- 55. Further results for eigenvalues of confining potential models.- References Chapter XVII.- XVIII Application of the FM to the Zeeman Effect in Hydrogen.- 56. Convergence of renormalized serie for the Landau regime.- 57. Further results for the Zeeman eigenvalues.- 58. FM approximation to the binding energy.- References Chapter XVIII.- XIX Application of the FM to the Stark Effect in Hydrogen.- 59. Approximation to Stark resonances.- 60. Upper and lower bound to the real part of the Stark resonances.- References Chapter XIX.- XX FM and Vibrational Potentials of Diatomic Molecules.- 61. Vibrational potentials for diatomic molecules.- 62. Kratzer-Fues potential and FM.- 63. Dunham series for ionic molecules.- 64. Dunham series for covalent molecules.- References Chapter XX.- Appendix A Scaling Laws of Schroedinger Operators.- Appendix B Applications of the Anharmonic Oscillator Model.- Appendix D Calculation of Integrals by the Saddle-Point Method.- Appendix E Construction of Pade Approximants.- Appendix F Normal Ordering of Operators.- Appendix G Applications of Models with Confining Potentials.- Appendix H Hamiltonian of an Hydrogen Atom in a Magnetic Field.- Appendix I Asymptotic Behavior of the Binding Energy for the Zeeman Effect in the Hydrogen Atom.- Appendix L RKR Method to Obtain Vibrational Potentials of Diatomic Molecules.- References Appendices A-L.
Series Title: Lecture notes in chemistry, 53.
Responsibility: G.A. Arteca, F.M. Fernández, E.A. Castro.
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