Two trapped particles interacting by a finite-ranged two-body potential in two spatial dimensions
Abstract
We examine the problem of two particles confined in an isotropic harmonic trap, which interact via a finite-ranged Gaussian-shaped potential in two spatial dimensions. We derive an approximative transcendental equation for the energy and study the resulting spectrum as a function of the interparticle interaction strength. Both the attractive and repulsive systems are analyzed. We study the impact of the potential's range on the ground-state energy. Complementary, we also explicitly verify by a variational treatment that in the zero-range limit the positive delta potential in two dimensions only reproduces the non-interacting results, if the Hilbert space in not truncated. Finally, we establish and discuss the connection between our finite-range treatment and regularized zero-range results from the literature.
Cite
@article{arxiv.1210.6701,
title = {Two trapped particles interacting by a finite-ranged two-body potential in two spatial dimensions},
author = {Rostislav A. Doganov and Shachar Klaiman and Ofir E. Alon and Alexej I. Streltsov and Lorenz S. Cederbaum},
journal= {arXiv preprint arXiv:1210.6701},
year = {2013}
}
Comments
19 pages, 5 figures, 1 table