Time-dependent invariants and stable coherent states

Ramachandran Vaidyanathan

Christopher C. Gerry

I.A. Malkin, Vladimir I. Man’ko, D. A. Trifonov

Xin Ma

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.

Prakash Chand

Fan Hong-Yi, Haider R. Zaidi

The conditions for the existence of a time-dependent invariant for the general quadratic Hamiltonian are investigated. A general expression for such an invariant is obtained, and it is shown that the stable squeezed states are eigenstates of this invariant.