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A class of solvable potentials

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Il Nuovo Cimento Series 10

Summary

A systematic method of constructing (velocity-independent) potentials, for which thes-wave Schrödinger equation can be solved in terms of known functions, is presented. Several such examples are constructed and the analytic structure of some of the corresponding scattering amplitudes worked out in detail. The use of Darboux’s theorem allows a significant extension of the class of solvable potentials.

Riassunto

Si presenta un metodo sistematico per costruire potenziali (indipendenti dalla velocità) per cui l’equazione di Schrödinger dell’ondas può essere risolta in termini di funzioni note. Si costruiscono molti esempi di questo tipo e si precisano le strutture analitiche di alcune delle corrispondenti ampiezze di scattering. L’uso del teorema di Darboux permette una significativa estensione della classe dei potenziali risolubili.

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References

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Authors and Affiliations

  1. University of Rochester, Rochester, N. Y.

    A. Bhattacharjie & E. C. G. Sudarshan

Authors
  1. A. Bhattacharjie
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  2. E. C. G. Sudarshan
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Supported in part by the U.S. Atomic Energy Commission.

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Bhattacharjie, A., Sudarshan, E.C.G. A class of solvable potentials. Nuovo Cim 25, 864–879 (1962). https://doi.org/10.1007/BF02733153

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  • DOI: https://doi.org/10.1007/BF02733153

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