On form-preserving transformations for the time-dependent Schr\"odinger equation
Finkel, Federico ; Gonzalez-Lopez, Artemio ; Kamran, Niky ; Rodriguez, Miguel A.
arXiv, 9809013 / Harvested from arXiv
Text on arXiv
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 Schr\"odinger 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 Schr\"odinger equation. Thus, any (real) potential solvable via a time-dependent Darboux transformation can alternatively be solved by applying an appropriate form-preserving transformation of the TDSE to a time-independent potential. The preeminent 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.
Publié le : 1998-09-15
Classification:  Mathematical Physics,  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  Quantum Physics,  81Q05, 81Q60 
@article{9809013,
     author = {Finkel, Federico and Gonzalez-Lopez, Artemio and Kamran, Niky and Rodriguez, Miguel A.},
     title = {On form-preserving transformations for the time-dependent Schr\"odinger
  equation},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9809013}
}

Finkel, Federico; Gonzalez-Lopez, Artemio; Kamran, Niky; Rodriguez, Miguel A. On form-preserving transformations for the time-dependent Schr\"odinger
  equation. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9809013/