Two-Body Atomic System in a One-Dimensional Anharmonic
Trap: The Energy Spectrum

I. S. Ishmukhamedov, D. T. Aznabayev, and S. A. Zhaugasheva

Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia

Al-Farabi Kazakh National University, Almaty, Kazakhstan

e-mail: ishmukh@theor.jinr.ru

Abstact—We numerically investigate the following two-body stationary Schrödinger equation (SE):

where x₁, x₂ , V(x_i) = V₀sin² (k_xx_i) is the potential describing the interaction of atoms with a trap and g(x₁ – x₂) is
the interatomic potential. Previously, a similar problem has been solved analytically for the harmonic interac-
tion V_h(x_i) = with the trap, which leads to the separation of coordinates y = x = for the
center-of-mass and relative motion. The anharmonicity of the trap couples these motions and, therefore, the
problem becomes significantly more complicated. In previous works, the anharmonicity V_a = V – V_h of the trap has
been taken into account in the framework of perturbation theory. In this work, the energy level shifts of a two-
body atomic system are calculated beyond the perturbation theory for different magnitudes of parameter g of
the interatomic interaction. The results are compared to those computed using the perturbation theory.

DOI: 10.1134/S1547477115050076

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