Abstract
We briefly review a class of nonlinear Schrödinger equations (NLS) which govern various physical phenomenon of Bose–Einstein condensation (BEC). We derive formulas for computing energy levels and wave functions of the Schrödinger equation defined in a cylinder without interaction between particles. Both fourth order and second order finite difference approximations are used for computing energy levels of 3D NLS defined in a cubic box and a cylinder, respectively. We show that the choice of trapping potential plays a key role in computing energy levels of the NLS. We also investigate multiple peak solutions for BEC confined in optical lattices. Sample numerical results for the NLS defined in a cylinder and a cubic box are reported. Specifically, our numerical results show that the number of peaks for the ground state solutions of BEC in a periodic potential depends on the distance of neighbor wells.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
