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Construction of the jost function and of the S-matrix for a general potential allowing solution of the Schrödinger equation in terms of hypergeometric functions

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Abstract

A general potential for which the one-dimensional Schrödinger equation is solvable in terms of hypergeometric functions is considered. Properties of Jost functions and of the S-matrix are investigated for vanishing angular momentum. The Green function of the problem is constructed for the limiting case corresponding to a confluent hypergeometric equation. The potential with a Coulomb asymptotic at infinity — a generalization of the ordinary Coulomb potential — is analyzed with particular detail.

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Literature cited

  1. P. M. Morse, Phys. Rev.,34, 57 (1929).

    Google Scholar 

  2. C. Eckart, Phys. Rev.,35, 1303 (1930).

    Google Scholar 

  3. G. A. Natanzon, Vestn. Leningr. Univ.,22, No. 10 (1971).

  4. A. K. Zaichenko and V. S. Ol'khovskii, Teor. Mat. Fiz.,27, 267 (1976).

    Google Scholar 

  5. S. S. Tokar' and Yu. K. Tomashuk, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 5, 27 (1975).

    Google Scholar 

  6. A. Hautot, Bull. Soc. Roy. Sci., Liège,43, 348 (1974).

    Google Scholar 

  7. A. Hautot, J. Math. Phys.,14, 1320 (1973).

    Google Scholar 

  8. G. Bencze, Comment. Phys. Math.,31, 1 (1966).

    Google Scholar 

  9. T. Tietz, J. Chem. Phys.,38, 3036 (1963).

    Google Scholar 

  10. T. Tietz, Acta Phys. Polon.,26, 353 (1964).

    Google Scholar 

  11. V. L. Bakhrakh and S. I. Vetchinkin, Teor. Mat. Fiz.,6, 392 (1971).

    Google Scholar 

  12. K. I. Ivanov, Nauchni Trudove, Fizika (Plovdiv),10, No. 1, 57 (1972).

    Google Scholar 

  13. R. G. Newton, Scattering Theory of Waves and Particles, McGraw-Hill (1966).

  14. M. F. Manning and N. Rosen, Phys. Rev.,44, 953 (1933).

    Google Scholar 

  15. N. Rosen and P. M. Morse, Phys. Rev.,42, 210 (1932).

    Google Scholar 

  16. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Vol. 2, McGraw-Hill (1953).

  17. G. Pöschl and E. Teller, Z. Phys.,83, 143 (1933).

    Google Scholar 

  18. G. A. Natanzon, Author's Abstract of Candidate's Dissertation, Leningrad (1974).

  19. L. Hülthen, Arkiv Math. Astron. Fys.,28A(5),29B(1) (1942).

  20. A. I. Baz' and Ya. B. Zel'dovich, Scattering, Reactions, and Decay in Nonrelativistic Quantum Mechanics [in Russian], Fizmatgiz, Moscow (1971).

    Google Scholar 

  21. S. I. Vetchinkin and V. L. Bachrach, Intern. J. Quant. Chem.,6, 143 (1972).

    Google Scholar 

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Authors and Affiliations

  1. Leningrad Hydrometeorological Institute, USSR

    G. A. Natanzon

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  1. G. A. Natanzon
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 23–28, July, 1978.

The author is grateful to A. K. Kazanskii for a number of critical remarks.

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Natanzon, G.A. Construction of the jost function and of the S-matrix for a general potential allowing solution of the Schrödinger equation in terms of hypergeometric functions. Soviet Physics Journal 21, 855–859 (1978). https://doi.org/10.1007/BF00892036

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  • DOI: https://doi.org/10.1007/BF00892036

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