%0 Journal Article
%A Finkel Morgenstern, Federico
%A González López, Artemio
%A Kamran, Niky
%A Rodríguez González, Miguel Ángel
%T On form-preserving transformations for the time-dependent Schrodinger equation
%D 1999
%@ 0022-2488
%U https://hdl.handle.net/20.500.14352/59670
%X 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.
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