Exact solutions for the D-dimensional spherical isotropic confined harmonic oscillator

2008/03/28 by H. E. Montgomery, Montgomery, H. E., G. Campoy +3
Computer Science · Engineering · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Gyrotron and Vacuum Electronics Research #Mathematical Physics (math-ph) #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.0803.4029

openalex publication_date 2008/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the size effect on the energy levels of the D-dimensional isotropic harmonic oscillator confined within a box of radius r_c with impenetrable walls. Two different approaches are used to obtain the energy eigenvalues and eigenfunctions for D=1,2,...,5. In the first we solve the Schroedinger equation exactly. In the second we use a series expansion of the wave function. The numerical results obtained are extremely accurate; these values are reported with 50 decimal places.

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