Harmonic oscillator in a one-dimensional box

TL;DR

This paper investigates a harmonic molecule confined in a one-dimensional box, comparing variational, perturbation, and numerical methods across different mass ratios and box sizes to understand its energy spectrum.

Contribution

It introduces suitable variational functions for the problem and provides a comprehensive comparison of approximate and accurate energies for various box sizes and mass configurations.

Findings

Variational and perturbation methods closely match numerical energies.

Energy behavior varies significantly between small and large box sizes.

Symmetry considerations influence the energy spectrum and solutions.

Abstract

We study a harmonic molecule confined to a one--dimensional box with impenetrable walls. We explicitly consider the symmetry of the problem for the cases of different and equal masses. We propose suitable variational functions and compare the approximate energies given by the variation method and perturbation theory with accurate numerical ones for a wide range of values of the box length. We analyze the limits of small and large box size.