Distributional Borel Summability of Odd Anharmonic Oscillators

TL;DR

This paper proves that the divergent perturbation series for odd anharmonic oscillators can be summed in a distributional sense to accurately identify the system's resonances.

Contribution

It introduces a distributional Borel summability method for divergent series in quantum oscillators, establishing a rigorous link to physical resonances.

Findings

Divergent series are Borel summable in the distributional sense.

Resonances are accurately recovered from the summation.

Applicable to all odd anharmonic oscillators.

Abstract

It is proved that the divergent Rayleigh-Schrodinger perturbation expansions for the eigenvalues of any odd anharmonic oscillator are Borel summable in the distributional sense to the resonances naturally associated with the system.