Author(s): F. Calogero (Eds.)
Series: Mathematics in Science and Engineering 35
Publisher: Academic Press
Year: 1967
Language: English
Pages: v-x, 1-244
Content:
Edited by
Page v
Copyright Page
Page vi
Foreword
Pages vii-ix
F. Calogero
Notation
Page x
1 Introduction
Pages 1-2
2 Review of scattering theory
Pages 3-7
3 Derivation of the phase equation
Pages 8-12
4 Discussion of the phase equation and of the behavior of the phase function. Procedures for the numerical computation of scattering phase shifts
Pages 13-20
5 The phase function. Examples
Pages 21-30
6 Connection between phase function and radial wave function. The amplitude function
Pages 31-36
7 Bounds on the scattering phase shift and on its variation with energy
Pages 37-42
8 Born approximation and improved Born approximation
Pages 43-47
9 Variational and extremum principles for evaluating scattering phase shifts
Pages 48-52
10 Born approximation, improved Born approximation, variational and extremum principles. Examples
Pages 53-66
11 Low-energy expansion. Scattering length and effective range. Bounds on the zero-energy cross section
Pages 67-76
12 The scattering length and its approximate and variational expressions. Examples
Pages 77-84
13 Generalized formulation of the phase method. Other types of phase equations
Pages 85-92
14 Simultaneous maximum and minimum principles for the evaluation of scattering phase shifts
Pages 93-96
15 Scattering on singular potentials. High-energy behavior and approximate expression of the scattering phase shift in this case
Pages 97-112
16 Further generalization of the phase method
Pages 113-119
17 Scattering of Dirac particles
Pages 120-128
18 Scattering on nonlocal potentials and on complex potentials
Pages 129-135
19 The multichannel case
Pages 136-142
20 Bound states. Discussion of the pole equation and of the behavior of the pole functions for q > 0
Pages 143-153
21 Behavior of pole functions and computation of binding energies. Examples
Pages 154-175
22 Relation between the number of bound states and the value of the scattering phase shift at zero energy (Levinson's theorem)
Pages 176-181
23 Bounds on the number and energies of bound states in a given potential. Necessary and sufficient conditions for the existence of bound states
Pages 182-197
Appendix I: Riccati-Bessel, Riccati-Hankel, and other functions
Pages 198-204
Appendix II: Variational and extremum principle for first-order differential equations
Pages 205-214
Appendix III: Asymptotic behavior of scattering phase shifts at large energy
Pages 215-220
Appendix IV: Derivation of the pole equation and discussion of the pole functions for q < 0
Pages 221-235
References Review Article
Pages 236-237
Bibliography Review Article
Pages 238-239
Author Index
Pages 241-242
Subject Index
Pages 243-244
