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15 February 2025
 
  » arxiv » 1609.0248

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Construction of Exact Ermakov-Pinney Solutions and Time-Dependent Quantum Oscillators
Sang Pyo Kim ; Won Kim ;
Date 1 Sep 2016
AbstractThe harmonic oscillator with a time-dependent frequency has a family of linear quantum invariants for the time-dependent Schr"{o}dinger equation, which are determined by any two independent solutions to the classical equation of motion. Ermakov and Pinney have shown that a general solution to the time-dependent oscillator with an inverse cubic term is expressed in terms of two independent solutions to the time-dependent oscillator. We explore the connection between linear quantum invariants and Ermakov-Pinney solution for the time-dependent harmonic oscillator. We advance a novel method to construct Ermakov-Pinney solutions to a class of time-dependent oscillators and the wave functions for time-dependent Schr"{o}dinger equation. We further show that the first and second P"{o}schl-Teller potentials belong to a special class of exact time-dependent oscillators.
Source arXiv, 1609.0248
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