2019/12/11 by Kevin Zelaya, K Zelaya, Véronique Hussin +1 · 1 citation
Mathematics · Physics and Astronomy · #Constant (computer programming) #Factorization #Harmonic oscillator #Mathematical functions and polynomials #Parametric equation #Parametric oscillator #Parametric statistics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum harmonic oscillator #Spectral Theory in Mathematical Physics #quant-ph
paper · pdf · doi:10.1088/1751-8121/ab78d1
published as J. Phys. A: Math. Theor. 53 (2020) 165301
arxiv created 2019/12/11 · openalex created_date 2019/12/26 · openalex publication_date 2020/02/21 · arxiv updated 2020/11/23 · openalex updated_date 2026/08/06
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 Schrödinger 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 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.