Scattering from a nonsymmetric potential in one dimension as a coupled-channel problem

American Journal of Physics

Volumn 64, Issue 7, 1996, Pages 923-928

  Nogami, Y ^a   Ross, C K ^b  

^a MCMASTER UNIVERSITY   (Canada)

^b NATIONAL RESEARCH COUNCIL CANADA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030549394     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18123     Document Type: Article

References (18)

1. J. H. Eberly, "Quantum scattering theory in one dimension," Am. J. Phys. 33, 771 (1965).
2. H. Lipkin, Quantum Mechanics (North-Holland, Amsterdam, 1973), Chap. 8.
3. M. Sassoli de Bianchi, "Levinson's theorem, zero-energy resonances, and time delay in one-dimensional scattering systems," J. Math. Phys. 35, 2719-2733 (1994).
4. J. M. Blatt and L. C. Biedenharn, "The angular distribution of scattering and reaction cross sections," Rev. Mod. Phys. 24, 258-272 (1952); N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions (Oxford U.P., London, 1965), Chap. 2 and 10.
5. J. M. Blatt and L. C. Biedenharn, "The angular distribution of scattering and reaction cross sections," Rev. Mod. Phys. 24, 258-272 (1952); N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions (Oxford U.P., London, 1965), Chap. 2 and 10.
6. P. Senn, "Threshold anomalies in one-dimensional scattering," Am. J. Phys. 56, 916-921 (1988).
7. 0(k)=0 for any value of k.
8. E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970), 2nd ed., Ch. 6.
9. R. G. Newton, "Inverse scattering. I. One dimension," J. Math. Phys. 21, 493-505 (1980); "Inverse scattering by a local impurity in a periodic potential in one dimension," J. Math. Phys. 24, 2152-2162 (1980); T. Aktosun and R. G. Newton, "Nonuniqueness in the one-dimensional inverse scattering problem," Inv. Prob. 1, 291-300 (1985).
10. R. G. Newton, "Inverse scattering. I. One dimension," J. Math. Phys. 21, 493-505 (1980); "Inverse scattering by a local impurity in a periodic potential in one dimension," J. Math. Phys. 24, 2152-2162 (1980); T. Aktosun and R. G. Newton, "Nonuniqueness in the one-dimensional inverse scattering problem," Inv. Prob. 1, 291-300 (1985).
11. R. G. Newton, "Inverse scattering. I. One dimension," J. Math. Phys. 21, 493-505 (1980); "Inverse scattering by a local impurity in a periodic potential in one dimension," J. Math. Phys. 24, 2152-2162 (1980); T. Aktosun and R. G. Newton, "Nonuniqueness in the one-dimensional inverse scattering problem," Inv. Prob. 1, 291-300 (1985).
12. G. Barton, "Levinson's theorem in one dimension: heuristics," J. Phys. A: Gen. Math. 18, 479-494 (1985).
13. S. Flügge, Practical Quantum Mechanics (Springer-Verlag, Berlin, 1974), Problem 39.
14. 3 Sassoli de Bianchi's derivation is based on the integrability of certain expressions involving phase shifts and mixing parameter, whereas ours is simply based on the observation that the Ts and Rs are all real at threshold.
15. The s-d mixing parameter of the nucleon-nucleon scattering vanishes at threshold. This is due to the centrifugal potential in the d-wave channel.
16. J. Formanek, "Phase shift analysis of one-dimensional scattering," Am. J. Phys. 44, 778-779 (1976). Fromanek used the example of Eq. (6.1) to show that Eberly's analysis is not sufficient when the potential is nonsymmetric.
17. W. Tobocman and M. Pauli, "Comparison of approximate methods for multiple scattering in high energy collisions," Phys. Rev. D 5, 2088-2101 (1972); K. K. Bajaj and Y. Nogami, "Scattering from many centers in one dimension." Can. J. Phys. 53, 874-881 (1974).
18. W. Tobocman and M. Pauli, "Comparison of approximate methods for multiple scattering in high energy collisions," Phys. Rev. D 5, 2088-2101 (1972); K. K. Bajaj and Y. Nogami, "Scattering from many centers in one dimension." Can. J. Phys. 53, 874-881 (1974).