Advertisement

Russian Physics Journal

, Volume 38, Issue 7, pp 706–712 | Cite as

Darboux transformation for the nonsteady Schrödinger equation

  • V. G. Bagrov
  • B. F. Samsonov
  • L. A. Shekoyan
Physics Of Elementary Particles And Field Theory

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.

Keywords

Steady State Quantum Mechanic Differential Operator Elementary Form Darboux Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. J. Fernandez and L. M. Nieto, J. Phys. A,27, 347 (1994).Google Scholar
  2. 2.
    F. M. Fernandez, A. L. Pineiro, and B. Moreno, J. Phys. A,27, 5013 (1994).Google Scholar
  3. 3.
    W. Schnizer and H. Leeb, J. Phys, A,27, 2605 (1994).Google Scholar
  4. 4.
    B. F. Samsonov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 3, 95 (1995).Google Scholar
  5. 5.
    B. F. Samsonov and I. N. Ovcharov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 7, 3 (1995).Google Scholar
  6. 6.
    M. J. Englefield, J. Phys. A,20, 593 (1987).Google Scholar
  7. 7.
    B. F. Samsonov and I. N. Ovcharov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 4, 77 (1995).Google Scholar
  8. 8.
    R. G. Agaeva, in: F. G. Maksudov and K. A. Rustamov (eds.), Modern Group Analysis. Methods and Applications [in Russian], Elm, Baku (1989), p. 3.Google Scholar
  9. 9.
    V. G. Bagrov, A. V. Shapovalov, and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 9, 19 (1991).Google Scholar
  10. 10.
    V. G. Bagrov, A. V. Shapovalov, and I. V. Shirokov, Teor. Mat. Fiz.,87, No. 3, 426 (1991).Google Scholar
  11. 11.
    V. G. Bagrov, A. V. Shapovalov, and I. V. Shirokov, Phys. Lett. A,147, No. 7, 348 (1990).Google Scholar
  12. 12.
    W. Miller, Symmetry and Variable Separation [Russian translation], Mir, Moscow (1981).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • V. G. Bagrov
  • B. F. Samsonov
  • L. A. Shekoyan

There are no affiliations available

Personalised recommendations