Time-dependent invariants and generalized coherent states

Ravinder Rupchand Puri, S. V. Lawande

Ramachandran Vaidyanathan

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.

Jung Kon Kim, Sang Pyo Kim

For a time-dependent harmonic oscillator with an inverse squared singular term, we find the generalized invariant using the Lie algebra of $SU(2)$ and construct the number-type eigenstates and the coherent states using the spectrum-generating Lie algebra of $SU(1,1)$. We obtain the evolution operator in both of the Lie algebras. The number-type eigenstates and the coherent states are constructed group-theoretically for both the time-independent and the time-dependent harmonic oscillators with the singular term. It is shown that the squeeze operator transforms unitarily the time-dependent basis of the spectrum-generating Lie algebra of $SU(1,1)$ for the generalized invariant, and thereby evolves the initial vacuum into a final coherent vacuum.

Luis Lorenzo Sánchez-Soto, Eusebio Bernabéu