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理论物理通讯：英文版

Application of Tripartite Entangled State Representation in Solving the Dynamics of a Kind of Three Coupled Oscillators

PANGQian-Jun

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

We study the eigenstate problem of a kind of three coupled oscillators in a new quantum mechanical representation composed by the spontaneous eigenvectors 〈p, q2, q3| for three operators (p1 +p2 +p3), (x3 - x2), and (x3 - x1). The eigenvalues and eigenvectors of the Hamiltonian are obtained. With the same method, the eigenstate problem of a generalized three-coupled oscillator Hamiltonian is studied, which has never been studied before.

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We study the eigenstate problem of a kind of three coupled oscillators in a new quantum mechanical representation composed by the spontaneous eigenvectors 〈p, q2, q3| for three operators (p1 +p2 +p3), (x3 - x2), and (x3 - x1). The eigenvalues and eigenvectors of the Hamiltonian are obtained. With the same method, the eigenstate problem of a generalized three-coupled oscillator Hamiltonian is studied, which has never been studied before.
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.