Solution of a two-dimensional time-dependent Schrödinger equation describing two interacting atoms in an optical trap
Ishmukhamedov I.S. Ishmukhamedov A.S. Jalankuzov Z.E.
2024Peoples Friendship University of Russia
Discrete and Continuous Models and Applied Computational Science
2024#32Issue 2172 - 180 pp.
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.
cold atoms , finite differences , Gaussian interaction potential , optical trap , pseudopotential , quantum harmonic oscillator , split operator method , time-dependent Schrödinger equation , zero-range interaction
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Institute of Nuclear Physics, Almaty, 050032, Kazakhstan
Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Institute of Nuclear Physics
Al-Farabi Kazakh National University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026