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College Physics

Exact solution for non-identical n modes coupled harmonic oscillators

Lu Huai

Published Jan 1, 2000• 1 citation
OpenAlex

Abstract

Energy spectrum of non-identical coupled harmonic oscillators is given by using quantum transformation theory.So,a general method is presented.

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理论物理通讯：英文版•Jan 1, 2001•0 citations
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.
Hamiltonian of two modes coupled harmonic oscillators is general quadric form of generalized coordinates and momenta.After coordinate transformation,it can be expressed as standard quadric form under new bases.Because canonical commutation relation is satisfied among new coordinates,creation operator and annihilation operator are introduced.Thus,coupling between modes is eliminated and Hamiltonian can be simplified as two mode independent harmonic oscillators,problem is solved.This method can be generalized in solving non-identical n modes coupled harmonic oscillators.