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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 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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참고문헌 (6)
참고문헌 신청
Bejoy K. Choudhury / 1995 / The Riemann zeta-function and its derivatives / Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci 450 : 477 ~ 499
C. Soule / 1992 / Lectures on Arakelov Geometry / Cambridge University Press : 94 ~ 101
Dr. Wilhelm Magnus / 1966 / The gamma function and related functions", Chapter 1, Formulas and Theorems for the Special Functions of Mathematical Physics / Springer-Verlag, Berlin
John Roe / 1999 / Elliptic Operators, Topology, and Asymptotic Methods / Chapman and Hall : 126 ~ 135
M. Dimassi / 1999 / Spectral Asymptotics in the Semi-Classical Limit / Cambridge University Press : 24 ~ 25
C. Soule / 1992 / Lectures on Arakelov Geometry / Cambridge University Press : 94 ~ 101
Dr. Wilhelm Magnus / 1966 / The gamma function and related functions", Chapter 1, Formulas and Theorems for the Special Functions of Mathematical Physics / Springer-Verlag, Berlin
John Roe / 1999 / Elliptic Operators, Topology, and Asymptotic Methods / Chapman and Hall : 126 ~ 135
M. Dimassi / 1999 / Spectral Asymptotics in the Semi-Classical Limit / Cambridge University Press : 24 ~ 25
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