Solution of a two-dimensional time-dependent Schrödinger equation describing two interacting atoms in an optical trap
Journal: Discrete and Continuous Models and Applied Computational Science (Vol.32, No. 2)Publication Date: 2024-11-02
Authors : I. Ishmukhamedov; A. Ishmukhamedov; Zh. Jalankuzov;
Page : 172-180
Keywords : split operator method; finite differences; time-dependent Schrödinger equation; quantum harmonic oscillator; Gaussian interaction potential; zero-range interaction; pseudopotential; cold atoms; 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.
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Last modified: 2024-11-02 04:40:31