Description of ultracold atoms in a one-dimensional geometry of a harmonic trap with a realistic interaction

We compute the ground state energy of two atoms in a one-dimensional geometry of a harmonic optical trap. We obtain a dependence of the energy on a one-dimensional scattering length, which corresponds to various strengths of the interaction potential of a gaussian type. The calculation is performed by numerical and analytical methods. For the analytical method we choose the oscillator representation method (OR), which has been successfully applied to computations of bound states of various few-body systems. The main results of this paper are: 1) numerical investigation of the validity range of the previously used pseudopotential method; 2) investigation of the validity range of the OR for a superposition of parabolic and gaussian potentials.