Quantum harmonic oscillator with time dependent mass
I. Ramos-Prieto, A. Espinosa-Z\'u\~niga, M. Fern\'andez-Guasti and, H.M. Moya-Cessa
TL;DR
This paper introduces a method to solve the quantum harmonic oscillator with a time-dependent mass by transforming it into a frequency-dependent problem and applying Lewis-Ermakov invariants, with specific examples of mass growth.
Contribution
It presents a novel approach using Fourier operators and Lewis-Ermakov invariants to analytically solve the time-dependent mass harmonic oscillator.
Findings
Successfully transforms the problem into a frequency-dependent oscillator.
Derives explicit solutions for quadratic and hyperbolic mass growth.
Provides analytical expressions for the wavefunctions under these mass variations.
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 Schr\"odinger equation by using squeeze operators. Finally we give two examples of time dependencies: quadratically and hyperbolically growing masses.
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