The Schr\"odinger system H=-{1/2}e^{\Upsilon(t-t_o)}\partial_{xx} +\lfrac{1}{2}\omega^2e^{-\Upsilon(t-t_o)}x^2

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) Schrodinger equation. We give the specific transformations to i) the more general quadratic (TQ) Schrodinger equation and to ii) a different time-dependent oscillator (TO) equation. For each Schrodinger system, we give the Lie algebra of space-time symmetries, the number states, the coherent states, the squeezed-states and the time-dependent , , (\Delta x)^2, (\Delta p)^2, and uncertainty product.