Solution of a two-dimensional time-dependent Schrödinger equation describing two interacting atoms in an optical trap

Abstract

We introduce a numerical method to solve the two-dimensional time-dependent Schrödinger equation, which characterizes a system of two atoms with a finite-range interaction potential confined within a harmonic oscillator trap. We choose a Gaussian-shaped potential for the interaction potential. Such a system has been previously studied analytically, except that a zero-range interaction potential was used instead. We observe a strong agreement between the results for the two types of interactions. Also, we investigate the one-dimensional time-dependent Schrödinger equation for the relative motion and compute the ground state energy level as a function of the coupling strength.

Keywords

• split operator method
• finite differences
• time-dependent schrödinger equation
• quantum harmonic oscillator
• gaussian interaction potential
• zero-range interaction
• pseudopotential
• cold atoms
• optical trap