Time-dependent perturbation theory in quantum mechanics and the renormalization group

Bhattacharjee, J. K. ; Ray, D. S. (2016) Time-dependent perturbation theory in quantum mechanics and the renormalization group American Journal of Physics, 84 (6). pp. 434-442. ISSN 0002-9505

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Official URL: http://doi.org/10.1119/1.4944701

Related URL: http://dx.doi.org/10.1119/1.4944701

Abstract

Time-dependent perturbation theory in quantum mechanics is divergent at long times when the perturbation induces a resonance between two eigenstates of the unperturbed Hamiltonian. Divergences in perturbation theory are also common in quantum field theory and in critical phenomena. The renormalization group (RG) was designed to deal with these divergences. In the last two decades, this procedure has been extended to dynamical systems where the perturbation theory diverges in the long-time limit. In this article, we first review the connection between RG in the context of field theory and RG in the context of dynamical systems. We then show that the long-time divergence in the resonant situation in the time-dependent perturbation theory in quantum mechanics can be removed by using a RG-aided calculational scheme.

Item Type:Article
Source:Copyright of this article belongs to American Association of Physics Teachers.
ID Code:133824
Deposited On:30 Dec 2022 09:39
Last Modified:30 Dec 2022 09:39

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