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Communications in Theoretical Physics

Energy Spectrum of a Bipartite Complicated-Coupled-Oscillator System

Pang Qian-Jun

Published Mar 1, 2006• 0 citations
Publisher

Abstract

We present a general discussion on the eigenstate problem of a bipartite complicated-coupled-oscillator system. By use of a generalized intermediate entangled state representation, the eigenvalue and eigenfunction of Hamiltonian are analytically obtained. As its application, we obtain the energy spectrum for two special situations of Hamiltonian.

DOI
10.1088/0253-6102/45/3/011

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We present a general discussion on the eigenstate problem of a bipartite complicated-coupled-oscillator system. By use of a generalized intermediate entangled state representation, the eigenvalue and eigenfunction of Hamiltonian are analytically obtained. As its application, we obtain the energy spectrum for two special situations of Hamiltonian.
We study the eigenstate problem of a two-coupled oscillator system. A new entangled state representation |γ composed of the common eigenvectors of operators (x1+p2) and (p1+x2) is established. Eigenvalues and eigenvectors of the Hamiltonian are obtained in |γ representations. The same problem is studied in the second-quantization representation. We find that the second-quantization representation can be used to derive the normally ordered product expression of eigenvector in Fock space. In particular, we find that the ground state of the Hamiltonian is a kind of generalized two-mode squeezed state.