Trial wave function approach to calculate the Ground state energy of nonlinear Schrodinger equation in many body physics

Document Type : Full length research Paper

Authors

1 Department of Mathematics, Faculty of Science, Qom University of technology, Qom, Iran

2 Department of Physics-Faculty of sciences-Qom University of Technology-Qom-Iran

Abstract

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.

Keywords

References

 
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Journal of Research on Many-body Systems
Volume 8, Issue 16
June 2018
Pages 73-82

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History

  • Receive Date: 05 July 2017
  • Revise Date: 11 September 2017
  • Accept Date: 30 December 2017

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