Quantum anharmonic oscillator and its statistical properties

TL;DR

This paper investigates a family of quantum anharmonic oscillators using Hermite functions, analyzing their eigenenergies and statistical properties, and comparing results with Random Matrix Theory predictions.

Contribution

It introduces a numerical approach to study quantum anharmonic oscillators and compares their eigenvalue statistics with theoretical models.

Findings

Eigenenergies are computed numerically for the family of oscillators.

Eigenvalue statistics align with Random Matrix Theory predictions.

Conclusions support the applicability of RMT to quantum anharmonic systems.

Abstract

In the present article a family of quantum anharmonic oscillators is studied using Hermite's function basis (Fock's basis) in the Hilbert space. The numerical investigation of the eigenenergies of that family is presented. The statistical properties of the calculated eigenvalues are compared with the theoretical predictions derived from the Random Matrix Theory. Conclusions are inferred.