  We present some general results for the time-dependent mass Hamiltonian
problem with H=-{1/2}e^{-2\nu}\partial_{xx} +h^{(2)}(t)e^{2\nu}x^2. This
Hamiltonian corresponds to a time-dependent mass (TM) Schr\"odinger equation
with the restriction that there are only P^2 and X^2 terms. We give the
specific transformations to a different quantum Schr\"odinger(TQ) equation and
to a different time-dependent oscillator (TO) equation. For each Schr\"odinger
system, we give the Lie algebra of space-time symmetries and (x,t)
representations for number states, coherent states, and squeezed states. These
general results include earlier work as special cases.
