Time-dependent Mass Schrödinger Equations. Ii. Example 1

In this paper, we attack the specific time-dependent Hamiltonian problem H = − 1 2 e Υ(t−to) ∂ xx + 1 2 ω 2 e −Υ(t−to) x 2. This corresponds to a time-dependent mass (T M) Schrödinger equation. We give the specific transformations to i) the more general quadratic (T Q) Schrödinger equation and to ii) a different time-dependent oscillator (T O) equation. For each Schrödinger 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, (∆x) 2 , (∆p) 2 , and uncertainty product.