  The Feynman path integral for the generalized harmonic oscillator is
reviewed, and it is shown that the path integral can be used to find a complete
set of wave functions for the oscillator. Harmonic oscillators with different
(time-dependent) parameters can be related through unitary transformations. The
existence of generalized coherent states for a simple harmonic oscillator can
then be interpreted as the result of a (formal) {\em invariance} under a
unitary transformation which relates the same harmonic oscillator. In the path
integral formalism, the invariance is reflected in that the kernels do not
depend on the choice of classical solutions.
