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Journal of Heze Teachers College

Energy Eigenvalue of the Double Dimension Coupling Harmonic Oscillator Was Solved Accurately by Transformation of Coordinates

Hongqi Li

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

Energy eigenvalue of the double dimension coupling harmonic oscillator was studied by transformation of coordinates. The common form of transformation matrix was given and the energy eigenvalue of the double dimension coupling boson harmonic oscillator was solved accurately .

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Based on the rotation transformation in the phase space and the technique of integration within an ordered product of operators,the coherent state representations of the rotation operator in quantum phase space,the Fourier transform operator and the parity operator are derived. Then the three-mode rotation operator is introduced.By the three-mode rotation operator,the Hamilton of the three-dimensional coordinate-momentum coupled harmonic oscillators is simply decoupled. Then its exact energy spectrums and eigenstates are obtained.