Exact diagonalization of the $d-$dimensional confined quantum harmonic oscillator
Quantum Physics
2016-04-22 v2 Mathematical Physics
math.MP
Abstract
In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as searching for the roots of hypergeometric functions or numerically solving a differential equation. In this paper, however, we derive an explicit matrix representation for the Hamiltonian of a confined quantum harmonic oscillator in higher dimensions, thus facilitating direct diagonalization.
Keywords
Cite
@article{arxiv.1604.01095,
title = {Exact diagonalization of the $d-$dimensional confined quantum harmonic oscillator},
author = {Kunle Adegoke and Adenike Olatinwo and Henry Otobrise and Funmi Akintujoye and Afees Tiamiyu},
journal= {arXiv preprint arXiv:1604.01095},
year = {2016}
}