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

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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.

About the authors

I. S. Ishmukhamedov

Institute of Nuclear Physics; Al-Farabi Kazakh National University

Author for correspondence.
Email: i.ishmukhamedov@mail.ru
ORCID iD: 0000-0002-7903-3432

Candidate of Physical and Mathematical Sciences

Almaty, 050032, Kazakhstan; Almaty, 050040, Kazakhstann

A. S. Ishmukhamedov

Institute of Nuclear Physics; Al-Farabi Kazakh National University

Email: altaymedoed@gmail.com
ORCID iD: 0000-0001-5248-3022

Researcher

Almaty, 050032, Kazakhstan; Almaty, 050040, Kazakhstann

Zh. E. Jalankuzov

Institute of Nuclear Physics; Al-Farabi Kazakh National University

Email: jalankuzov.zhanibek@gmail.com
ORCID iD: 0009-0003-1962-8834

Researcher

Almaty, 050032, Kazakhstan; Almaty, 050040, Kazakhstann

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