Abstract We study the eigenstate problem of a two-coupled oscillator system. A new entangled state representation $\left\vert \gamma \right\rangle $ composed of the common eigenvectors of operators $% (x_{1}+p_{2})$ and $(p_{1}+x_{2})$ is established. Eigenvalues and eigenvectors of the Hamiltonian are obtained in $\left\vert \gamma \right\rangle $ 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.
Received: 09 October 2004
Revised: 04 March 2005
Accepted manuscript online:
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