Compact versus noncompact quantum dynamics of time-dependent su(1,1)-valued Hamiltonians

We consider the Schrodinger problem for time-dependent (TD) Hamiltonians represented by a linear combination of the compact generator and the hyperbolic generator of su(1, 1). Several types of transitions, characterized by different time initial conditions on the generator coefficients, are analyzed by resorting to the harmonic oscillator model with a frequency vanishing for t --> infinity. We provide examples that point out how the TD states of the transitions can be constructed either by the compact eigenvector basis or by the noncompact eigenvector basis depending on the initial conditions characterizing the frequency time behavior. (C) 1996 Academic Press, Inc.