Time - dependent mass Schrödinger equations . III . Example

We attack the specific time-dependent Hamiltonian problem H = − 2 ( to t a ∂xx+ 1 2ω 2 ( t to )b x2. This corresponds to a time-dependent mass (TM) Schrödinger equation. We give the specific transformations to a different time-dependent quadratic Schrödinger equations (TQ) and to a different time-dependent oscillator (TO) equation. For each Schrödinger system, we give the Lie algebra of space-time symmetries, the number states, the squeezed-state 〈x〉 and 〈p〉 (with their classical motion), (∆x)2, (∆p)2, and the uncertainty product. PACS: 03.65.-w, 02.20.+b, 42.50.-p Email: [email protected] Email: [email protected]