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Finkel Morgenstern, Federico and González López, Artemio and Kamran, Niky and Rodríguez González, Miguel Ángel (1999) On formpreserving transformations for the timedependent Schrodinger equation. Journal of mathematical physics, 40 (7). pp. 32683274. ISSN 00222488

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Official URL: http://dx.doi.org/10.1063/1.532885
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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 timedependent Schroumldinger equation (TDSE). In our main result, we prove that any pair of timedependent real potentials related by a Darboux transformation for the TDSE may be transformed by a suitable point transformation into a pair of timeindependent potentials related by a usual Darboux transformation for the stationary Schroumldinger equation. Thus, any (real) potential solvable via a timedependent Darboux transformation can alternatively be solved by applying an appropriate formpreserving point transformation of the TDSE to a timeindependent potential. The preeminent role of the latter type of transformations in the solution of the TDSE is illustrated with a family of quasiexactly solvable timedependent anharmonic potentials.
Item Type:  Article 

Additional Information:  © 1999 American Institute of Physics. 
Subjects:  Sciences > Physics > PhysicsMathematical 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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