  In this paper, we attack the specific time-dependent Hamiltonian problem
H=-{1/2}e^{\Upsilon(t-t_o)}\partial_{xx}
+\lfrac{1}{2}\omega^2e^{-\Upsilon(t-t_o)}x^2. This corresponds to a
time-dependent mass (TM) Schr\"odinger equation. We give the specific
transformations to i) the more general quadratic (TQ) Schr\"odinger equation
and to ii) a different time-dependent oscillator (TO) equation. For each
Schr\"odinger system, we give the Lie algebra of space-time symmetries, the
number states, the coherent states, the squeezed-states and the time-dependent
<x>, <p>, (\Delta x)^2, (\Delta p)^2, and uncertainty product.
