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: mmn@lanl.gov Email: truax@ucalgary.ca

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@inproceedings{Nieto2008TimeD, title={Time - dependent mass Schr{\"{o}dinger equations . III . Example}, author={Michael Martin Nieto and Rodney Truax}, year={2008} }