Strong-Weak Coupling Duality in Quantum Mechanics

TL;DR

This paper introduces a strong-weak coupling duality in quantum mechanics that maps strongly coupled problems to weakly coupled ones, enabling exact solutions and insights into energy spectra of polynomial potentials.

Contribution

It establishes a duality framework in quantum mechanics analogous to quantum field theory, allowing analysis of nonperturbative regimes and exact solutions for certain potentials.

Findings

Duality maps strong coupling to weak coupling regimes.

Exact solutions for power-type potentials.

Insights into energy spectra of polynomial potentials.

Abstract

We present a strong-weak coupling duality for quantum mechanical potentials. Similarly to what happens in quantum field theory, it relates two problems with inverse couplings, leading to a mapping of the strong coupling regime into the weak one, giving information from the nonperturbative region of the parameters space. It can be used to solve exactly power-type potentials and to extract deep information about the energy spectra of polynomial ones.