The two-body problem of ultra-cold atoms in a harmonic trap

TL;DR

This paper solves the two-body problem for ultra-cold bosonic atoms in a harmonic trap, revealing a universal energy spectrum independent of the interaction potential's shape, as long as its range is small.

Contribution

It provides an exact solution to the two-body problem in a harmonic trap, demonstrating universality of the energy spectrum for ultra-cold atoms with short-range interactions.

Findings

Energy spectrum is universal for short-range interactions.

Exact solutions are obtained for the two-body problem.

Universality holds regardless of interaction potential shape.

Abstract

We consider two bosonic atoms interacting with a short-range potential and trapped in a spherically symmetric harmonic oscillator. The problem is exactly solvable and is relevant for the study of ultra-cold atoms. We show that the energy spectrum is universal, irrespective of the shape of the interaction potential, provided its range is much smaller than the oscillator length.