[en] We attack the specific time-dependent Hamiltonian problem H=-((1)/(2))(((t_o)/(t)))^a∂_xx+((1)/(2))ω²(((t)/(t_o)))^bx². This corresponds to a time-dependent mass (TM) Schroedinger equation. We give the specific transformations to a different time-dependent quadratic Schroedinger equation (TQ) and to a different time-dependent oscillator (TO) equation. For each Schroedinger system, we give the Lie algebra of space-time symmetries, the number states, the squeezed-state < x> and < p> (with their classical motion), (Δx)², (Δp)², and the uncertainty product