The zeta-determinants of harmonic oscillators on R^2

Title
The zeta-determinants of harmonic oscillators on R^2
Authors
김경화
Keywords
thezetadeterminantsofharmonicoscillatorsonr2
Issue Date
2011
Publisher
인하대학교
Abstract
The zeta-determinant of a differential operator is a global spectral invariant which plays an important role in geometry, topology and mathematical physics. In this thesis we compute the zeta-determinants of harmonic oscillators defined on R^2 For this purpose we start from investigating basic properties of harmonic oscillators including their spectra and eigenfunctions. Using change of variables we reduce harmonic oscillators with general quadratic forms to the standard form of harmonic oscillators and compute their spectra and eigenfunctions. Finally, we review the definition of the zeta-determinant and compute the zeta-determinants of harmonic oscillators by using the Riemann zeta function, Hurwitz zeta function and Gamma function.
Description
1.Introduction 1 2.Basic harmonic oscillator 3 3.The harmonic oscillators with quadratic potential 9 4.The zeta-determinant of H(a,b) 26
URI
http://dspace.inha.ac.kr/handle/10505/22568
Appears in Collections:
College of Natural Science(자연과학대학) > Mathematics (수학) > Theses(수학 석박사 학위논문)
Files in This Item:
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