Exactly Solvable Time-Dependent Oscillator-Like Potentials Generated by Darboux Transformations

Abstract

The stationary Schroedinger equation of the harmonic oscillator is deformed by a Darboux transformation to construct time-dependent potentials with the oscillator profile. The Darboux (supersymmetric or factorization) method is usually developed in the spatial variables of the Schroedinger equation. Here we follow a variation introduced by Bagrov, Samsonov and Shekoyan to include the time-variable as a parameter of the transformation.

6 pages, 8 figures. Based on the work presented by K. Zelaya in the Quantum Fest 2016: International Conference on Quantum Phenomena, Quantum Control and Quantum Optics, 17-21 October 2016, Mexico City, Mexico

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