Wavefunctios of log-periodic oscillators

Abstract

We use the Lewis and Riesenfeld invariant method [\textit{J. Math. Phys.} \textbf{10}, 1458 (1969)] 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 $m=m_{0}t/t_0$ and $\omega ={\omega }_0{t}_0/t$, which exhibits an exact log-periodic oscillation, behaves as the harmonic oscillator with $m$ and $\omega$ constant.

15 pages, 3 figures

References in corpus (1)

• Applications of Lie systems in dissipative Milne--Pinney equations