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Darboux transformation and elementary exact solutions of the Schrödinger equation

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Abstract

Darboux transformation is applied to three classical potentials, namely the harmonic oscillator, effective Coulomb and Morse potentials to generate exactly solvable potentials of elementary form. For every potential, the isospectral families of potentials are constructed. For almost all potentials, a set of normalized discrete spectrum wave functions is given.

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Author notes

  1. Vladislav G Bagrov

    Present address: Electronics Institute, 4 Akademichesky Ave, 634 055, Tomsk, Russia

Authors and Affiliations

  1. Tomsk State University, 36 Lenin Ave, 634 050, Tomsk, Russia

    Vladislav G Bagrov & Boris F Samsonov

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  1. Vladislav G Bagrov
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  2. Boris F Samsonov
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Bagrov, V.G., Samsonov, B.F. Darboux transformation and elementary exact solutions of the Schrödinger equation. Pramana - J Phys 49, 563–580 (1997). https://doi.org/10.1007/BF02848330

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  • DOI: https://doi.org/10.1007/BF02848330

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