Application of Coordinate-Momentum Intermediate Representation in Solving Eigenstate Problem of a Coupled Oscillator System

We study the eigenstate problem of a kind of coupled oscillators in the new quantum mechanical represen-tationi <q,μ,v>, which is defined as the eigenvector of the operator (μQ + vP), whereμ and v are two real parameters. Wealso use the U operator transformation method to deal with the same problem. We obtain the normally ordered productexpressions of U operator and eigenvector. It is shown that the ground state of system Hamiltonian is a squeezed state.