Simple simulation for electron energy levels in geometrical potential wells

TL;DR

This paper introduces a simple simulation program that models electron energy levels and wavefunctions in three-dimensional geometrical potential wells with various shapes, aiding quantum mechanical analysis of quantum dots.

Contribution

The paper presents an octopus program capable of generating electron energy levels and wavefunctions in geometrical potential wells with different shapes, matching quantum dot energies.

Findings

Successfully simulated ground and excited state energies.

Produced wavefunctions for degeneracy and vibrational mode analysis.

Adjusted electron mass fraction for accurate energy matching.

Abstract

An octopus program is demonstrated to generate electron energy levels in three-dimensional geometrical potential wells. The wells are modeled to have shapes similar to cone, pyramid and truncated-pyramid. To simulate the electron energy levels in quantum mechanical scheme like the ones in parabolic band approximation scheme, the program is run initially to find a suitable electron mass fraction that can produce ground-state energies in the wells as close to those in quantum dots as possible and further to simulate excited-state energies. The programs also produce wavefunctions for exploring and determining their degeneracies and vibrational normal modes.