Time-dependent invariants and stable unitarily transformed coherent states.

Abstract

For the Hamiltonian of a single mode of an electromagnetic field that preserves coherent states, the general form of the time-dependent Hermitian invariant, of which a given stable coherent state is an eigenstate, is obtained with an appropriate initial condition. The result may be generalized to give a similar invariant for a Hamiltonian that preserves any particular class of unitarily transformed coherent states such as squeezed states.