Wave functions of log-periodic oscillators

Journal Article · Wed Jun 15 00:00:00 EDT 2011 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3601739· OSTI ID:21501348

Bessa, V; Guedes, I ^[1]

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1. Departamento de Fisica, Universidade Federal do Ceara, Campus do Pici, Fortaleza, CE 60455-760 (Brazil)

We use the Lewis and Riesenfeld invariant method [J. Math. Phys. 10, 1458 (1969)] and a unitary transformation to obtain the exact Schroedinger 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{sub 0}t/t{sub 0} and {omega}={omega}{sub 0}t{sub 0}/t, which exhibits an exact log-periodic oscillation, behaves as the harmonic oscillator with m and {omega} constant.

• OSTI ID: 21501348
• Journal Information: Journal of Mathematical Physics, Vol. 52, Issue 6; Other Information: DOI: 10.1063/1.3601739; (c) 2011 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
COORDINATES
CORRELATIONS
FLUCTUATIONS
HARMONIC OSCILLATORS
OSCILLATORS
PERIODICITY
SCHROEDINGER EQUATION
TIME DEPENDENCE
TRANSFORMATIONS
WAVE FUNCTIONS
DIFFERENTIAL EQUATIONS
ELECTRONIC EQUIPMENT
EQUATIONS
EQUIPMENT
FUNCTIONS
PARTIAL DIFFERENTIAL EQUATIONS
VARIATIONS
WAVE EQUATIONS