Two trapped particles interacting by a finite-range two-body potential in two spatial dimensions

Rostislav A. Doganov, Shachar Klaiman, Ofir E. Alon, Alexej I. Streltsov, Lorenz S. Cederbaum

Research output: Contribution to journalArticlepeer-review


We examine the problem of two particles confined in an isotropic harmonic trap, which interact via a finite-range 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. We also explicitly verify by a variational treatment that in the zero-range limit the positive δ potential in two dimensions only reproduces the noninteracting results, if the Hilbert space in not truncated, and demonstrate that an extremely large Hilbert space is required to approach the ground state when one is to tackle the limit of zero-range interaction numerically. Finally, we establish and discuss the connection between our finite-range treatment and regularized zero-range results from the literature. The present results indicate that a finite-range interparticle potential is numerically amenable for treating the statics and the nonequilibrium dynamics of interacting many-particle systems (bosons) in two dimensions.

Original languageEnglish
Article number033631
Number of pages8
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number3
StatePublished - 28 Mar 2013

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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