新纠缠态表象对耦合2谐振子系统的应用

我们研究一个耦合2谐振子系统的本征态问题。我们构造了由算子（x1+p2）和（x2+p1）的共同本征态组成的新纠缠态表象︱γ>。在︱γ>表象得到了系统哈密顿的本征值和本征态。同样的问题用二次量子化表象进行了研究。我们发现在Fock空间，二次量子化表象可以被用来推得本征态的正规积表示。特别是发现了系统基态为广义2模压缩态

Application of new entangled state representation to a two-coupled oscillator system

We study the eigenstate problem of a two-coupled oscillator system. A new entangled state representation $leftvert gamma rightrangle $ 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 $leftvert gamma rightrangle $ representations. The same problem is studied in the second-quantization representation. We find that the second-quantization representation can beused 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.