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Article overview
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Construction of Exact Ermakov-Pinney Solutions and Time-Dependent Quantum Oscillators | Sang Pyo Kim
; Won Kim
; | Date: |
1 Sep 2016 | Abstract: | The 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 | Services: | Forum | Review | PDF | Favorites |
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