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American Journal of Physics

Methods of establishing the asymptotic behavior of the harmonic oscillator wave functions

Marshall A. Bowen, Joseph Coster

Published Apr 1, 1980• 5 citations
Publisher
DOI
10.1119/1.12149

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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.