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理论物理通讯：英文版

Energy Level of Three-Mode Harmonic Oscillator for Coordinate Operators Satisfying Cyclic Commutative Relations Obtained by IEO Method

Wu, Yang Hao, Fan, Hong-Yi

Published Jan 1, 2008• 0 citations
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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.
Through coordinate transformation,Hamiltonian of N modes coupled harmonic oscillators could be expressed as the standard quadric form in new bases to eliminate the coupled items.As a result of calculation,a fact could be found that the new bases satisfy quasi-canonical commutation relation.By introducing quasi-particle’s creation and annihilation operators,the Hamiltonian could be simplified as N modes independent harmonic oscillators.Furthermore,the corresponding eigenvalues and eigenfunction could be obtained.