Solution of a two-dimensional time-dependent Schrödinger equation describing two interacting atoms in an optical trap
- Authors: Ishmukhamedov I.S.1,2, Ishmukhamedov A.S.1,2, Jalankuzov Z.E.1,2
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Affiliations:
- Institute of Nuclear Physics
- Al-Farabi Kazakh National University
- Issue: Vol 32, No 2 (2024)
- Pages: 172-180
- Section: Articles
- URL: https://journal-vniispk.ru/2658-4670/article/view/316829
- DOI: https://doi.org/10.22363/2658-4670-2024-32-2-172-180
- EDN: https://elibrary.ru/CRIVYI
- ID: 316829
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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, KazakhstannA. 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, KazakhstannZh. 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, KazakhstannReferences
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