No abstract

We present exact solutions of a class of the nonlinear models which describe the parametric conversion of photons. Hamiltonians of these models are related to the classes of finite orthogonal polynomials. The spectra and exact expressions for eigenvectors of these Hamiltonians are obtained.

In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states related to these systems is constructed and described. Some applications are also presented.

The one-mode and the two-mode multiboson systems with sl(2,R) symmetry are investigated.Hamiltonians of these systems are integrated using the theory of orthogonal polynomials. The coherent state representation for these systems is constructed.Comment: 23 pages, 1 figur