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arXiv · 1912.05643

Time-dependent rational extensions of the parametric oscillator: quantum invariants and the factorization method

Kevin Zelaya·Véronique Hussin
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Abstract

New families of time-dependent potentials related to the parametric oscillator are introduced. This is achieved by introducing some general time-dependent operators that factorize the appropriate constant of motion (quantum invariant) of the parametric oscillator, leading to new families of quantum invariants that are almost-isospectral to the initial one. Then, the respective time-dependent Hamiltonians are constructed, and the solutions of the Schr\"odinger equation are determined from the intertwining relationships and by finding the appropriate time-dependent complex-phases of the Lewis-Riesenfeld approach. To illustrate the results, the set of parameters of the new potentials are fixed such that a family of time-dependent rational extensions of the parametric oscillator is obtained. Moreover, the rational extensions of the harmonic oscillator are recovered in the appropriate limit.

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Kevin Zelaya, Véronique Hussin. 2019-12-11. Time-dependent rational extensions of the parametric oscillator: quantum invariants and the factorization method. https://doi.org/10.1088/1751-8121/ab78d1

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