An Alternative Perturbative Expansion in Quantum Mechanics. Scaling and cut-off Resummation

TL;DR

This paper introduces a new perturbative expansion method in quantum mechanics for the anharmonic oscillator, utilizing a scaling and cut-off resummation technique to improve convergence and accurately compute ground state energies at large couplings.

Contribution

It presents a novel perturbative expansion that exploits scaling arbitrariness and employs a cut-off resummation method to enhance convergence in quantum mechanical calculations.

Findings

Improved convergence of perturbative series for anharmonic oscillator energies.

Effective resummation technique using energy cut-off.

Accurate asymptotic ground state energy calculations at large couplings.

Abstract

An alternative perturbative expansion in quantum mechanics which allows a full expression of the scaling arbitrariness is introduced. This expansion is examined in the case of the anharmonic oscillator and is conveniently resummed using a method which consists in introducing an energy cut-off that is carefully removed as the order of the expansion is increased. We illustrate this technique numerically by computing the asymptotic behavior of the ground state energy of the anharmonic oscillator for large couplings, and show how the exploitation of the scaling arbitrariness substantially improves the convergence of this perturbative expansion.