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http://dx.doi.org/10.11568/kjm.2011.19.2.129

THE ZETA-DETERMINANTS OF HARMONIC OSCILLATORS ON R2  

Kim, Kyounghwa (Department of Mathematics Inha University)
Publication Information
Korean Journal of Mathematics / v.19, no.2, 2011 , pp. 129-147 More about this Journal
Abstract
In this paper we discuss the zeta-determinants of harmonic oscillators having general quadratic potentials defined on $\mathbb{R}^2$. By using change of variables we reduce the harmonic oscillators having 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.
Keywords
zeta-determinant; harmonic oscillator; quadratic potential;
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