Korean J. Math.  Vol 19, No 2 (2011)  pp.
DOI: https://doi.org/10.11568/kjm.2011.19.2.

THE ZETA-DETERMINANTS OF HARMONIC OSCILLATORS ON $\mathbb{R}^2$

Kyounghwa Kim

Abstract


In this paper we discuss the zeta-determinants of harmonic oscillators having general quadratic potentials defined on R^2. By using change of variables we reduce the harmonic oscillators hav- ing general quadratic potentials to the standard harmonic oscillators and compute their spectra and eigenfunctions. We then discuss their zeta functions and zeta-determinants. In some special cases we compute the zeta-determinants of harmonic oscillators concretely by using the Riemann zeta function, Hurwitz zeta function and Gamma function. 


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ISSN: 1976-8605 (Print), 2288-1433 (Online)

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