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arXiv · 2512.23517

Van der Waals interaction at short and long distances: a pedagogical path from stationary to time-dependent perturbation theory

L. Saba·C. D. Fosco
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Abstract

The van der Waals interaction between neutral atoms is typically studied using stationary perturbation theory for the short-distance (London) limit, while long-distance (Casimir-Polder) results are usually derived via semiclassical, time-dependent approaches. Here, we demonstrate that reformulating stationary perturbation theory calculations in terms of time-ordered correlation functions significantly simplifies the mathematical treatment. This reformulation is particularly advantageous for higher-order calculations required in the long-distance regime, where retardation effects become important. Our approach provides a unified framework connecting both limiting cases, and is intended as a bridge between advanced quantum mechanics and field-theoretic treatments of dispersion forces, suitable for graduate-level courses or specialized readers.

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L. Saba, C. D. Fosco. 2025-12-29. Van der Waals interaction at short and long distances: a pedagogical path from stationary to time-dependent perturbation theory. https://doi.org/10.1088/1361-6404%2Fae8891

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