Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)4138610.22363/2658-4670-2024-32-2-172-180CRIVYIArticlesСтатьиResearch ArticleSolution of a two-dimensional time-dependent Schrödinger equation describing two interacting atoms in an optical trapРешение двумерного нестационарного уравнения Шрёдингера, описывающего два взаимодействующих атома в оптической ловушкеhttps://orcid.org/0000-0002-7903-3432IshmukhamedovI. S.ИшмухамедовИ. С.

Candidate of Physical and Mathematical Sciences

i.ishmukhamedov@mail.ruhttps://orcid.org/0000-0001-5248-3022IshmukhamedovA. S.ИшмухамедовА. С.

Researcher

altaymedoed@gmail.comhttps://orcid.org/0009-0003-1962-8834JalankuzovZh. E.ДжаланкузовЖ. Е.

Researcher

jalankuzov.zhanibek@gmail.comInstitute of Nuclear PhysicsИнститут ядерной физикиAl-Farabi Kazakh National UniversityКазахский национальный университет им. аль-Фараби15102024322VOL 32, NO2 (2024)ТОМ 32, №2 (2024)17218001112024Copyright ©; 2024, Ishmukhamedov I.S., Ishmukhamedov A.S., Jalankuzov Z.E.Copyright ©; 2024, Ишмухамедов И.С., Ишмухамедов А.С., Джаланкузов Ж.Е.2024Ishmukhamedov I.S., Ishmukhamedov A.S., Jalankuzov Z.E.Ишмухамедов И.С., Ишмухамедов А.С., Джаланкузов Ж.Е.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/miph/article/view/41386

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.

Мы представляем численный метод решения двумерного нестационарного уравнения Шредингера, которое характеризует систему двух атомов с потенциалом взаимодействия конечного радиуса действия, заключенную в ловушку гармонического осциллятора. В качестве потенциала взаимодействия мы выбираем гауссовский потенциал. Такая система ранее изучалась аналитически, с той лишь разницей, что вместо нее использовался нулевой потенциал взаимодействия. Мы наблюдаем хорошее согласие между результатами для двух типов взаимодействий. Кроме того, мы исследуем одномерное нестационарное уравнение Шредингера для относительного движения и вычисляем уровень энергии основного состояния в зависимости от константы связи.

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