Generalized Borel Transform Technique in Quantum Mechanics

TL;DR

The paper introduces the Generalized Borel Transform (GBT), a novel method for approximating solutions in quantum mechanics that works effectively across different energy regimes, outperforming traditional techniques.

Contribution

It presents the GBT as a new approach capable of handling both perturbative and non-perturbative regimes in quantum mechanics, with demonstrated efficiency.

Findings

GBT accurately captures low and high energy behaviors

Compared favorably with standard Borel sum methods

Effective in a solvable quantum mechanics model

Abstract

We present the Generalized Borel Transform (GBT). This new approach allows one to obtain approximate solutions of Laplace/Mellin transform valid in both, perturbative and non perturbative regimes. We compare the results provided by the GBT for a solvable model of quantum mechanics with those provided by standard techniques, as the conventional Borel sum, or its modified versions. We found that our approach is very efficient for obtaining both the low and the high energy behavior of the model.