Time-dependent rational extensions of the parametric oscillator: quantum invariants and the factorization method
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.
Keywords
Cite
@article{arxiv.1912.05643,
title = {Time-dependent rational extensions of the parametric oscillator: quantum invariants and the factorization method},
author = {Kevin Zelaya and Véronique Hussin},
journal= {arXiv preprint arXiv:1912.05643},
year = {2020}
}