The absolute definition of the phase-shift in potential scattering

Journal of Mathematical Physics

Volumn 42, Issue 9, 2001, Pages 4031-4049

  Chadan, Khosrow ^a   Kobayashi, Reido ^b   Kobayashi, Takao ^b  

^a UNIVERSITÉ PARIS SUD   (France)

^b TOKYO UNIVERSITY OF SCIENCE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035537166     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1389090     Document Type: Article

References (13)

1. R. G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (Springer-Verlag, Berlin, 1982).
2. A. Galindo and P. Pascual, Quantum Mechanics (Springer-Verlag, Berlin, 1990) 2 volumes.
3. K. Chadan and P. Sabatier, Inverse Problems in Quantum Scattering Theory, 2nd ed. (Springer-Verlag, Berlin, 1989).
4. W. Frank and D. J. Land, "Singular potentials," Rev. Mod. Phys. 43, 36-98 (1971).
5. N. Fröman and K. E. Thylwe, "Setting the question of the high energy behavior of phase-shifts," J. Math. Phys. 20, 1716-1719 (1979).
6. O. Brander, "High-energy behavior of phase-shifts for scattering from singular potentials," J. Math. Phys. 22, 1229-1235 (1981).
7. F. Calogero, Variable Phase Approach to Potential Scattering (Academic, New York, 1967). See especially Chap. 3, and Chap. 6, formulas (3) and (8). A complete list of references is given in this book.
8. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions.
9. K. Chadan, N. N. Khuri, A. Martin, and T. T. Wu, "Universality of low-energy scattering in 2 + 1 dimensions," Phys. Rev. D 58, 025014-1-19 (1998).
10. E. Hille, Lectures on Ordinary Differential Equations (Addison-Wesley, Reading, MA, 1969).
11. E.-A. Coddington and N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1955).
12. K. Chadan in An Introduction to Inverse Scattering and Inverse Spectral Problems, edited by K. Chadan, D. Colton, L. Päivärinta and W. Rundell (SIAM, Philadelphia, 1997).
13. E. C. Titchmarsh, Theory of Fourier Integrals, 2nd ed. (Oxford University Press, Oxford 1962), pp. 172-173, theorems 126 and 127 combined together.