The Schrödinger system H=-{1/2} (t_o/t)^a \partial_{xx} + (1/2) ω^2 (t/t_o)^b x^2
arXiv:quant-ph/9911095 · doi:10.1006/aphy.2001.6145
Abstract
We attack the specific time-dependent Hamiltonian problem H=-{1/2} (t_o/t)^a \partial_{xx} + (1/2) ω^2 (t/t_o)^b x^2. 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), (Δx)^2, (Δp)^2, and the uncertainty product.
LaTeX, 26 pages, including 3 figures and 13 tables. New title and format for journal. Conclusion added