  We construct an explicit solution of the Cauchy initial value problem for the
n-dimensional Schroedinger equation with certain time-dependent Hamiltonian
operator of a modified oscillator. The dynamical SU(1,1) symmetry of the
harmonic oscillator wave functions, Bargmann's functions for the discrete
positive series of the irreducible representations of this group, the Fourier
integral of a weighted product of the Meixner-Pollaczek polynomials, a
Hankel-type integral transform and the hyperspherical harmonics are utilized in
order to derive the corresponding Green function. It is then generalized to a
case of the forced modified oscillator. The propagators for two models of the
relativistic oscillator are also found. An expansion formula of a plane wave in
terms of the hyperspherical harmonics and solution of certain infinite system
of ordinary differential equations are derived as a by-product.
