Abstract
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.
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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, 2023, Vol. 215, pp. 111–120 https://doi.org/10.4213/tmf10399.
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Bedida, N., Fadhel, S., Difallah, M. et al. Quantum Coulomb problem in a Gaussian time-dependent electric field within the path integral formalism. Theor Math Phys 215, 551–559 (2023). https://doi.org/10.1134/S0040577923040062
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DOI: https://doi.org/10.1134/S0040577923040062