Geodesic
Quantum Coulomb problem in a~Gaussian time-dependent electric field within the~path integral formalism
Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 1, pp. 111-120

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We solve the Coulomb problem in nonrelativistic quantum mechanics with a charge depending on a parameter that plays the role of time. The choice of this dependence is needed, for example, after certain spatio–temporal transformations when dealing with the interaction of a “small” system (quantum sub-system) with a “large” system, e.g., a bath. These spatio–temporal transformations, combined with path integral, allow us to find the Feynman propagator of the quantum subsystem. To test our approach, we derive the pure Coulomb Green's function as a limit of our result.
Keywords: path integral, Green's function, modified Coulomb potential.
Mots-clés : perturbation series 
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     title = {Quantum {Coulomb} problem in {a~Gaussian} time-dependent electric field within the~path integral formalism},
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N. Bedida; S. Fadhel; M. Difallah; M. Meftah. Quantum Coulomb problem in a~Gaussian time-dependent electric field within the~path integral formalism. Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 1, pp. 111-120. http://geodesic.mathdoc.fr/item/TMF_2023_215_1_a5/