Quantum harmonic oscillator with time-dependent mass

Abstract

We use the Fourier operator to transform a time dependent mass quantum harmonic oscillator into a frequency dependent one. Then we use Lewis-Ermakov invariants to solve the Schrödinger equation by using squeeze operators. Finally we give two examples of time dependencies: quadratically and hyperbolically growing masses.

A Real Expectation Value of the Time-dependent Non-Hermitian Hamiltonians*

“…In section 3, we illustrate our formalism introduced in the previous section by treating a non-Hermitian time-dependent quantum oscillator with time-dependent mass in linear complex time-dependent potential. On the hand, in the Hermitian case the time-dependent quantum harmonic have been extensively studied in the literature in different ways [41][42][43][44][45][46][47][48]. Finally, section 4 concludes our work.…”

Bohm potential for the time dependent harmonic oscillator

“…Also algebraic methods to obtain the evolution operator have been shown [12]. They have been solved under various scenarios such as time dependent mass [12,13,14], time dependent frequency [15,11] and applications of invariant methods have been studied in different regimes [16]. Such invariants may be used to control quantum noise [17] and to study the propagation of light in waveguide arrays [18,19].…”

Engineering two-mode squeezed vacuum-like states by using the Bohm potential

“…Generation of two mode squeezed vacuum states and in particular of the superposition of two-mode squeezed states [4][5][6] may be used for quantum information processing and quantum sensing [7]. Coupled time dependent harmonic oscillators may be studied by using Ermakov-Lewis [8][9][10][11] (invariant) techniques as done by several authors [12][13][14]. In this manuscript we look at the problem of generation of two-moded squeezed states by shaping the phase of the wavefunction.…”