Path Integral Solution of a Class of Explicitly Time-Dependent Potentials

Details Path Integral Solution of a Class of Explicitly Time-Dependent Potentials Path Integral Solution of a Class of Explicitly Time-Dependent Potentials

1993-02-13

arxiv.org/abs/hep-th/9302054v2

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, amstex, SISSA/2/93/FM (In the revised version some improvements and corrections have been made.)

Scientific paper

10.1016/0375-9601(93)90048-5

A specific class of explicitly time-dependent potentials is studied by means of path integrals. For this purpose a general formalism to treat explicitly time-dependent space-time transformations in path integrals is sketched. An explicit time-dependent model under consideration is of the form $V(q,t)=V[q/\zeta(t)]/\zeta^2(t)$, where $V$ is a usual potential, and $\zeta(t)=(at^2+2bt+c)^{1/2}$. A recent result of Dodonov et al.\ for calculating corresponding propagators is incorporated into the path integral formalism by performing a space-time transformation. Some examples illustrate the formalism.

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