Wavefunctios of log-periodic oscillators

Details Wavefunctios of log-periodic oscillators Wavefunctios of log-periodic oscillators

2012-01-31

arxiv.org/abs/1201.6607v1

J. Math. Phys. 52, 062106 (2011)

Physics

Quantum Physics

15 pages, 3 figures

Scientific paper

10.1063/1.3601739

We use the Lewis and Riesenfeld invariant method [\textit{J. Math. Phys.} \textbf{10}, 1458 (1969)] and a unitary transformation to obtain the exact Schr\"{o}dinger 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 $m=m_0t/t_0$ and $\omega= \omega_0t_0/t$, which exhibits an exact log-periodic oscillation, behaves as the harmonic oscillator with $m$ and $\omega$ constant.

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