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Wave functions of log-periodic oscillators

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10.1063/1.3601739

### Abstract

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* = *m* _{0} *t*/*t* _{0} and ω = ω_{0} *t* _{0}/*t*, which exhibits an exact log-periodic oscillation, behaves as the harmonic oscillator with *m* and ω constant.

© 2011 American Institute of Physics

Received 24 March 2011
Accepted 24 May 2011
Published online 27 June 2011

Article outline:

I. INTRODUCTION

II. THE LEWIS AND RIESENFELD INVARIANT METHOD – WAVE FUNCTIONS FOR A TIME-DEPENDENT HARMONIC OSCILLATOR

III. WAVE FUNCTIONS OF TIME-DEPENDENT LOG-PERIODIC OSCILLATORS

A. and

B. and

C. and

IV. CONCLUDING REMARKS

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2011-06-27

2014-04-24

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