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Darboux transformation for the nonsteady Schrödinger equation

  • Physics Of Elementary Particles And Field Theory
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Abstract

The Darboux transformation for a nonsteady one-dimensional Schrödinger equation is introduced; its operator is an N-th order differential operator that converts the solution of an equation with a specified potential to a solution with a new potential constructed from the solutions of the initial equation. A relation is established between this transformation and supersymmetric quantum mechanics. Operators of time-conserved supercharge are introduced; for steady states, they reduce to the well-known operators. Examples of accurately solvable nonsteady potentials of elementary form are given.

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Authors
  1. V. G. Bagrov
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  2. B. F. Samsonov
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  3. L. A. Shekoyan
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Additional information

Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 59–65, July, 1995.

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Bagrov, V.G., Samsonov, B.F. & Shekoyan, L.A. Darboux transformation for the nonsteady Schrödinger equation. Russ Phys J 38, 706–712 (1995). https://doi.org/10.1007/BF00560273

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  • DOI: https://doi.org/10.1007/BF00560273

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