The 1/N Expansion in Noncommutative Quantum Mechanics

TL;DR

This paper investigates the 1/N expansion in noncommutative quantum mechanics, demonstrating good convergence for anharmonic potentials but divergence for Coulomb potentials, and proposes a modified potential to address this issue.

Contribution

It introduces a modified noncommutative Coulomb potential that yields a well-behaved 1/N expansion, improving the theoretical framework.

Findings

Good convergence for anharmonic oscillator

Divergent expansion for standard Coulomb potential

Modified potential achieves stable 1/N expansion

Abstract

We study the 1/N expansion in noncommutative quantum mechanics for the anharmonic and Coulombian potentials. The expansion for the anharmonic oscillator presented good convergence properties, but for the Coulombian potential, we found a divergent large N expansion when using the usual noncommutative generalization of the potential. We proposed a modified version of the noncommutative Coulombian potential which provides a well-behaved 1/N expansion.