An analysis of states in the phase space: the anharmonic oscillator

TL;DR

This paper presents a quantum model for analyzing anharmonic oscillators, calculating their energy levels and frequencies, with potential applications to lattice vibrations and other oscillating systems.

Contribution

It introduces a general quantum approach based on the uncertainty principle to analyze anharmonic oscillators, extending previous theoretical work.

Findings

Harmonic energy levels split into complex systems of levels

Energy levels depend on the number of anharmonic terms

Model applicable to various oscillating systems

Abstract

The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the properties of quantum systems exploiting the uncertainty principle only. For clarity the anharmonic oscillator is described having in mind the lattice oscillations of atoms/ions, yet quantum formalism of the model and approach have general character and can be extended to any oscillating system. The results show that the harmonic energy levels split into a complex system of energy levels dependent upon the number of anharmonic terms that characterize the oscillator.