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

Abstract

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 $\zeta (t)=(a{t}^2+2bt+c{)}^{1/2}$. 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.

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

References in corpus (1)

• Quantum Mechanics with Explicit Time Dependence

Cited by in corpus (7)

• $\delta$-Function Perturbations and Boundary Problems by Path Integration
• Quantum Dynamics in a Time-dependent Hard-Wall Spherical Trap
• Path Integration and Separation of Variables in Spaces of Constant Curvature in Two and Three Dimensions
• Path integral for a pair of time-dependent coupled and driven oscillators
• Resonant Population Transfer in the Time-Dependent Quantum Elliptical Billiard
• Fast Converging Path Integrals for Time-Dependent Potentials I: Recursive Calculation of Short-Time Expansion of the Propagator
• Fast Converging Path Integrals for Time-Dependent Potentials II: Generalization to Many-body Systems and Real-Time Formalism