Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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THE ZETA-DETERMINANTS OF HARMONIC OSCILLATORS ON R2

  • Received : 2011.01.25
  • Accepted : 2011.06.03
  • Published : 2011.06.30
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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.

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References

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