عنوان مقاله [English]
In this paper, we have studied some nonlinear Schrodinger equations appeared inmany body systems such as a nanowire with a soft polar layer, a quantum well in the presence of the electron-electron interactions, Grass-Pitaevskii equation for Bose-Einstein condensate in the presence on the two and three body interactions. Calculation of the ground state energy of these systems by analytical methods is very difficult. Solution of these equations through numerical methods like self-consistent one also needs complicated computer programming. In this paper, Ground state energy have been obtained by means of the Euler-Lagrange Variational method as well as simple and appropriate trial wave-functions.Comparison of the result we have obtained with the Varational technique and the available methods in the literatures shows the high accuracy ofthis method.
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