Variable Phase Approach to Potential Scattering

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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