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Physical Review A

Exact wave functions of a harmonic oscillator with time-dependent mass and frequency

I. A. Pedrosa

Published Apr 1, 1997• 189 citations
Publisher

Abstract

We use the Lewis and Riesenfeld invariant method [J. Math. Phys. 10, 1458 (1969)] to obtain the exact Schr"odinger wave functions for a harmonic oscillator with time-dependent mass and frequency. Exact coherent states for such system are also constructed.
DOI
10.1103/physreva.55.3219

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We use the Lewis and Riesenfeld invariant method [J. Math. Phys. 10, 1458 (1969)]10.1063/1.1664991 and a unitary transformation to obtain the exact Schrödinger wave functions for time-dependent harmonic oscillators exhibiting log-periodic-type behavior. For each oscillator we calculate the quantum fluctuations in the coordinate and momentum as well as the quantum correlations between the coordinate and momentum. We observe that the oscillator with m = m0t/t0 and ω = ω0t0/t, which exhibits an exact log-periodic oscillation, behaves as the harmonic oscillator with m and ω constant.
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