Separation of Variables and Exactly Soluble Time-Dependent Potentials in Quantum Mechanics

Details Separation of Variables and Exactly Soluble Time-Dependent Potentials in Quantum Mechanics Separation of Variables and Exactly Soluble Time-Dependent Potentials in Quantum Mechanics

1993-06-13

arxiv.org/abs/hep-th/9306060v1

Phys.Rev. A48 (1993) 2301

Physics

High Energy Physics

High Energy Physics - Theory

REVTEX, 30 pages, CLNS-93/1188, HWS-9313

Scientific paper

We use separation of variables as a tool to identify and to analyze exactly soluble time-dependent quantum mechanical potentials. By considering the most general possible time-dependent re-definition of the spatial coordinate, as well as general transformations on the wavefunctions, we show that separation of variables applies and exact solubility occurs only in a very restricted class of time-dependent models. We consider the formal structure underlying our findings, and the relationship between our results and other work on time-dependent potentials. As an application of our methods, we apply our results to the calculations of propagators.

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