  Based on the Gaussian wave packet solution for the harmonic oscillator and
the corresponding creation and annihilation operators, a generalization is
presented that also applies for wave packets with time-dependent width as they
occur for systems with different initial conditions, time-dependent frequency
or in contact with a dissipative environment. In all these cases the
corresponding coherent states, position and momentum uncertainties and quantum
mechanical energy contributions can be obtained in the same form if the
creation and annihilation operators are expressed in terms of a complex
variable that fulfills a nonlinear Riccati equation which determines the
time-evolution of the wave packet width. The solutions of this Riccati equation
depend on the physical system under consideration and on the (complex) initial
conditions and have close formal similarities with general superpotentials
leading to isospectral potentials in supersymmetric quantum mechanics. The
definition of the generalized creation and annihilation operator is also in
agreement with a factorization of the operator corresponding to the Ermakov
invariant that exists in all cases considered.
