Feinberg-Horodecki States of Time-Dependent Mass Distribution Harmonic Oscillator
Mahdi Eshghi, Ramazan Sever, Sameer M. Ikhdair
TL;DR
This paper solves the Feinberg-Horodecki equation for a harmonic oscillator with a time-dependent mass, deriving analytical stationary states and wave functions using the asymptotic iteration method, and analyzing their relation to standard oscillators.
Contribution
It introduces an analytical approach to solve the FH equation for TDM harmonic oscillators using AIM, providing explicit expressions for energies and wave functions.
Findings
Derived analytical stationary state energies and wave functions.
Showed solutions reduce to standard harmonic oscillator when mass variation is negligible.
Provided spectrum of stationary energies for TDM harmonic oscillators.
Abstract
The solution of the Feinberg-Horodecki (FH) equation for a time-dependent mass (TDM) harmonic oscillator quantum system is studied. A certain interaction is applied to a mass to provide a particular spectrum of stationary energies. The related spectrum of the harmonic oscillator potential acting on the TDM oscillators is found. We apply the time version of the asymptotic iteration method (AIM) to calculate analytical expressions of the TDM stationary state energies and their wave functions. It is shown that the obtained solutions reduce to those of simple harmonic oscillator as the time-dependent of the mass reduces to
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