Quantum anharmonic oscillator and its statistical properties in the first quantization scheme

TL;DR

This paper investigates the eigenenergies of quantum anharmonic oscillators across various dimensions using first quantization, comparing their statistical properties with predictions from Random Matrix theory.

Contribution

It introduces a detailed analysis of quantum anharmonic oscillators' eigenenergies in multiple dimensions within the first quantization framework, linking their statistics to Random Matrix theory.

Findings

Eigenenergy distributions align with Random Matrix theory predictions

Statistical properties vary with spatial dimension

Conclusions support theoretical models

Abstract

A family of quantum anharmonic oscillators is studied in any finite spatial dimension in the scheme of first quantization and the investigation of their eigenenergies is presented. The statistical properties of the calculated eigenenergies are compared with the theoretical predictions inferred from the Random Matrix theory. Conclusions are derived.