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Finkel Morgenstern, Federico and González López, Artemio and Kamran, Niky and Rodríguez González, Miguel Ángel (1999) On form-preserving transformations for the time-dependent Schrodinger equation. Journal of mathematical physics, 40 (7). pp. 3268-3274. ISSN 0022-2488
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Official URL: http://dx.doi.org/10.1063/1.532885
Abstract
In this paper we point out a close connection between the Darboux transformation and the group of point transformations which preserve the form of the time-dependent Schroumldinger equation (TDSE). In our main result, we prove that any pair of time-dependent real potentials related by a Darboux transformation for the TDSE may be transformed by a suitable point transformation into a pair of time-independent potentials related by a usual Darboux transformation for the stationary Schroumldinger equation. Thus, any (real) potential solvable via a time-dependent Darboux transformation can alternatively be solved by applying an appropriate form-preserving point transformation of the TDSE to a time-independent potential. The pre-eminent role of the latter type of transformations in the solution of the TDSE is illustrated with a family of quasi-exactly solvable time-dependent anharmonic potentials.
Item Type: | Article |
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Additional Information: | © 1999 American Institute of Physics. |
Subjects: | Sciences > Physics > Physics-Mathematical models Sciences > Physics > Mathematical physics |
ID Code: | 31405 |
Deposited On: | 29 Jul 2015 10:29 |
Last Modified: | 10 Dec 2018 15:10 |
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