Interacting particles in two dimensions: numerical solution of the four-dimensional Schrödinger equation in a hypercube
| dc.creator | Vanyolos, Andras | |
| dc.creator | Varga, Gabor | |
| dc.date | 2008-08-28 | |
| dc.date.accessioned | 2026-07-07T09:59:09Z | |
| dc.date.available | 2026-07-07T09:59:09Z | |
| dc.description | We study numerically the Coulomb interacting two-particle stationary states of the Schrödinger equation, where the particles are confined in a two-dimensional infinite square well. Inside the domain the particles are subjected to a steeply increasing isotropic harmonic potential, resembling that in a nucleus. For these circumstances we have developed a fully discretized finite difference method of the Numerov-type that approximates the four-dimensional Laplace operator, and thus the whole Schrödinger equation, with a local truncation error of $\mathcal{O}(h^6)$, with $h$ being the uniform step size. The method is built on a 89-point central difference scheme in the four-dimensional grid. As expected from the general theorem by Keller [Num.\ Math. \textbf{7}, 412 (1965)], the error of eigenvalues so obtained are found to be the same order of magnitude which we have proved analytically as well. | |
| dc.description | 44 pages, 28 figures | |
| dc.identifier | https://arxiv.org/abs/0808.3976 | |
| dc.identifier | http://arxiv.org/abs/0808.3976 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167927 | |
| dc.subject | Quantum Physics | |
| dc.title | Interacting particles in two dimensions: numerical solution of the four-dimensional Schrödinger equation in a hypercube | |
| dc.type | text |