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Physical Review A

Evolution of quantum systems driven by a Hamiltonian written in terms of the SU(1,1) group generators

G. Dattoli, A. Torre, R. Caloi

Published Apr 1, 1986• 22 citations
Publisher

Abstract

In this paper we exploit the Wei-Norman algebraic disentangling procedure to study the evolution of quantum states driven by a time-dependent Hamiltonian linear combination of the generators of the SU(1,1) group.
DOI
10.1103/physreva.33.2789

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We study the time evolution of a quantum system with Hamiltonian consisting of time-dependent linear combination of SU(1,1) and SU(2) generators. A proper hermitian invariant operator has been found to obtain not only closed formulas for the time evolution of quantum states but also the time evolution operators for both the SU(1, 1) and SU(2) systems. The time evolution operators have been used to investigate the time-dependent two photons and SU(2) squeezing states and squeezing properties of the time-dependent SU(1,1) coherent states.
We study the time evolution of quantum systems with a time-dependent Hamiltonian given by a linear combination of SU(1,1) and SU(2) generators. The invariant Hermitian operator is constructed in the same manner as for both the SU(1,1) and SU(2) systems. With the help of the invariant Hermitian operator we obtain not only the exact solutions of the Schr\"odinger equation but also the time-evolution operator. The adiabatic and nonadiabatic Berry phases are calculated with the exact solutions. \textcopyright{} 1996 The American Physical Society.