A Primer on Resonances in Quantum Mechanics

TL;DR

This paper provides a comprehensive overview of resonances in classical and quantum mechanics, covering theoretical concepts, mathematical methods, and applications such as electromagnetic refraction and quantum decay processes.

Contribution

It introduces key mathematical techniques like complex scaling and Darboux transformation for analyzing resonances in various physical systems.

Findings

Resonances are fundamental in understanding radiative reactions and electromagnetic wave refraction.

Mathematical methods like Fourier transform and complex scaling are effective in studying resonant states.

The paper connects classical and quantum resonance phenomena through pedagogical explanations.

Abstract

After a pedagogical introduction to the concept of resonance in classical and quantum mechanics, some interesting applications are discussed. The subject includes resonances occurring as one of the effects of radiative reaction, the resonances involved in the refraction of electromagnetic waves by a medium with a complex refractive index, and quantum decaying systems described in terms of resonant states of the energy. Some useful mathematical approaches like the Fourier transform, the complex scaling method and the Darboux transformation are also reviewed.