On form-preserving transformations for the time-dependent Schrödinger equation

@article{Finkel1998OnFT,
  title={On form-preserving transformations for the time-dependent Schr{\"o}dinger equation},
  author={Federico Finkel and Artemio Gonz{\'a}lez-L{\'o}pez and Niky Kamran and Miguel A. Rodriguez},
  journal={Journal of Mathematical Physics},
  year={1998},
  volume={40},
  pages={3268-3274}
}
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 Schrodinger 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 Schrodinger equation… 

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