On the two-dimensional harmonic oscillator with an electric field confined to a circular box

TL;DR

This paper investigates the energy spectrum of a 2D harmonic oscillator with an electric field inside a circular box, using numerical and perturbative methods, and compares results with previous studies.

Contribution

It provides a comprehensive analysis of the energy spectrum using Rayleigh-Ritz and perturbation theory, highlighting the effects of confinement and electric field.

Findings

Energy spectrum depends on box size and electric field strength

Rayleigh-Ritz method effectively computes energy levels

Results agree with previous studies within certain limits

Abstract

We revisit the quantum-mechanical two-dimensional harmonic oscillator with an electric field confined to a circular box of impenetrable walls. In order to obtain the energy spectrum we resort to the Rayleigh-Ritz method with polynomial and Gaussian basis sets. We compare present results with those derived recently by other authors. We discuss the limits of large and small box radius and also do some calculations with perturbation theory.