RT Journal Article
T1 On form-preserving transformations for the time-dependent Schrodinger equation
A1 Finkel Morgenstern, Federico
A1 González López, Artemio
A1 Kamran, Niky
A1 Rodríguez González, Miguel Ángel
AB 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.
PB American Institute of Physics
SN 0022-2488
YR 1999
FD 1999-07
LK https://hdl.handle.net/20.500.14352/59670
UL https://hdl.handle.net/20.500.14352/59670
LA eng
NO © 1999 American Institute of Physics.F.F., A.G.-L., and M.A.R. would like to acknowledge the partial financial support of the DGICYT under Grant No. PB95-0401. N.K. was supported in part by NSERC Grant No. 0GP0105490.
NO DGICYT
NO NSERC
DS Docta Complutense
RD 9 abr 2025