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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Cited by in corpus (8)

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• Coherent states for exactly solvable time-dependent oscillators generated by Darboux transformations
• Quantum nonstationary oscillators: Invariants, dynamical algebras and coherent states via point transformations
• Coherent and squeezed states: introductory review of basic notions, properties and generalizations
• Time-dependent rational extensions of the parametric oscillator: quantum invariants and the factorization method
• Fourth Painlevé and Ermakov equations: quantum invariants and new exactly-solvable time-dependent Hamiltonians
• Infinite square-well, trigonometric Pöschl-Teller and other potential wells with a moving barrier