Friday, October 26, 2012

1210.6701 (Rostislav A. Doganov et al.)

Two trapped particles interacting by a finite-ranged two-body potential
in two spatial dimensions
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Rostislav A. Doganov, Shachar Klaiman, Ofir E. Alon, Alexej I. Streltsov, Lorenz S. Cederbaum
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.
View original: http://arxiv.org/abs/1210.6701

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