Wave functions of log-periodic oscillators
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Publication:5266031
DOI10.1063/1.3601739zbMath1317.81094arXiv1201.6607OpenAlexW1989821874MaRDI QIDQ5266031
Publication date: 29 July 2015
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Abstract: We use the Lewis and Riesenfeld invariant method [ extit{J. Math. Phys.} extbf{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.
Full work available at URL: https://arxiv.org/abs/1201.6607
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Time-dependent Schrödinger equations and Dirac equations (35Q41)
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Quasi-coherent states for damped and forced harmonic oscillator ⋮ Shannon entropy, Fisher information and uncertainty relations for log-periodic oscillators
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