Umfang:
Online Ressource (x, 244 pages)
Ausgabe:
Online-Ausg.
ISBN:
012155550X
,
9780121555504
Serie:
Mathematics in Science and Engineering v. 35
Inhalt:
Review of scattering theory -- Derivation of the phase equation -- Discussion of the phase equation and of the behavior of the phase function : procedures for the numerical computation of scattering phase shifts -- Phase function, examples -- Connection between phase function and radial wave function : the amplitude function -- Bounds on the scattering phase shift and on its variation with energy -- Born approximation and improved Born approximation -- Variational and extremum principles for evaluationg scattering phase shifts -- Born approximation, improved Born approximation, variational and extremum principles -- Low-energy expansion, scattering length and effective range, bounds on the zero-energy cross section -- Scattering length and its approximate and variational expressions -- Scattering length and its approximate and variational expressions -- Generalized formulation of the phase method, other types of phase equations -- Simultaneous maximum and minimum principles for the evaluation of scattering phase shifts -- Scattering on singular potentials, high-energy behavior and approximate expression of the scattering phase shift in this case -- Further generalization of the phase method -- Scattering of Dirac particles -- Scattering on nonlocal potentials and on complex potentials -- Multichannel case -- Bound states, discussion of the pole equation and of the behavior of the pole functions for q〉 0 -- Behavior of pole functions and computation of binding energies -- Relation between the number of bound states and the value of the scattering phase shift at zero energy (Levinson's theorem) -- Bounds on the number and energies of bound states in a given potential, necessary and sufficient conditions for the existence of bound states
Anmerkung:
Includes bibliographical references and indexes. - Print version record
,
Front Cover; Variable Phase Approach to Potential Scattering; Copyrght Page; Contents; Foreword; Notation; Chapter 1. Introduction; Chapter 2. Review of Scattering Theory; Chapter 3. Derivation of the Phase Equation; Chapter 4. Discussion of the Phase Equation and of the Behavior of the Phase Function. Procedures for the Numerical Computation of Scattering Phase Shifts; Chapter 5. The Phase Function. Examples; Chapter 6. Connection Between Phase Function and Radial Wave Function. The Amplitude Function; Chapter 7. Bounds on the Scattering Phase Shift and on Its Variation with Energy
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Chapter 8. Born Approximation and Improved Born ApproximationChapter 9. Variational and Extremum Principles for Evaluating Scattering Phase Shifts; Chapter 10. Born Approximation, Improved Born Approximation, Variational and Extremum Principles. Examples; Chapter 11. Low-Energy Expansion. Scattering Length and Effective Range. Bounds on the Zero-Energy Cross Section; Chapter 12. The Scattering Length and Its Approximate and Variational Expressions. Examples; Chapter 13. Generalized Formulation of the Phase Method. Other Types of Phase Equations
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Chapter 14. Simultaneous Maximum and Minimum Principles for the Evaluation of Scattering Phase ShiftsChapter 15. Scattering on Singular Potentials. High-Energy Behavior and Approximate Expression of the Scattering Phase Shift in This Case; Chapter 16. Further Generalization of the Phase Method; Chapter 17. Scattering of DiracParticles; Chapter 18. Scattering on Nonlocal Potentials and on Complex Potentials; Chapter 19. The Multichannel Case; Chapter 20. Bound States. Discussion of the Pole Equation and of the Behavior of the Pole Functions for q 〉 0
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Chapter 21. Behavior of Pole Functions and Computation of Binding Energies. ExamplesChapter 22. Relation between the Number of Bound States and the Value of the Scattering Phase Shift at Zero Energy (Levinson's Theorem); Chapter 23. Bounds on the Number and Energies of Bound States in a Given Potential. Necessary and Sufficient Conditions for the Existence of Bound States; Appendix I. Riccati-Bessel, Riccati-Hankel, and Other Functions; Appendix II. Variational and Extremum Principle for First-Order Differential Equations
,
Appendix III. Asymptotic Behavior of Scattering Phase Shifts at Large EnergyAppendix IV. Derivation of the Pole Equation and Discussion of the Pole Functions for q 〈 0; References; Bibliography; Author Index; Subject Index;
,
Review of scattering theory -- Derivation of the phase equation -- Discussion of the phase equation and of the behavior of the phase function : procedures for the numerical computation of scattering phase shifts -- Phase function, examples -- Connection between phase function and radial wave function : the amplitude function -- Bounds on the scattering phase shift and on its variation with energy -- Born approximation and improved Born approximation -- Variational and extremum principles for evaluationg scattering phase shifts -- Born approximation, improved Born approximation, variational and extremum principles -- Low-energy expansion, scattering length and effective range, bounds on the zero-energy cross section -- Scattering length and its approximate and variational expressions -- Scattering length and its approximate and variational expressions -- Generalized formulation of the phase method, other types of phase equations -- Simultaneous maximum and minimum principles for the evaluation of scattering phase shifts -- Scattering on singular potentials, high-energy behavior and approximate expression of the scattering phase shift in this case -- Further generalization of the phase method -- Scattering of Dirac particles -- Scattering on nonlocal potentials and on complex potentials -- Multichannel case -- Bound states, discussion of the pole equation and of the behavior of the pole functions for q 〉 0 -- Behavior of pole functions and computation of binding energies -- Relation between the number of bound states and the value of the scattering phase shift at zero energy (Levinson's theorem) -- Bounds on the number and energies of bound states in a given potential, necessary and sufficient conditions for the existence of bound states.
Weitere Ausg.:
ISBN 012155550X
Sprache:
Englisch
Fachgebiete:
Physik
Schlagwort(e):
Electronic books
Mehr zum Autor:
Calogero, Francesco 1935-
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