Time-dependent Schrödinger Equations Having Isomorphic Symmetry Algebras. I. Classes of Interrelated Equations
نویسندگان
چکیده
In this paper, we focus on a general class of Schrödinger equations that are time-dependent and quadratic in X and P . We transform Schrödinger equations in this class, via a class of time-dependent mass equations, to a class of solvable timedependent oscillator equations. This transformation consists of a unitary transformation and a change in the “time” variable. We derive mathematical constraints for the transformation and introduce two examples. PACS: 03.65.-w, 02.20.+b, 42.50.-p Email: [email protected] Email: [email protected]
منابع مشابه
Time-dependent Schrödinger Equations Having Isomorphic Symmetry Algebras. Ii. Symmetry Algebras, Coherent and Squeezed States
Using the transformations from paper I, we show that the Schrödinger equations for: (1) systems described by quadratic Hamiltonians, (2) systems with time-varying mass, and (3) time-dependent oscillators, all have isomorphic Lie space-time symmetry algebras. The generators of the symmetry algebras are obtained explicitly for each case and sets of numberoperator states are constructed. The algeb...
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