Investigation of generalized distribution function via statistical mechanical methods
Project no. 24029 · Status: Kapanmış · 2022
Summary
<p>This work examines Bose-Einstein condensation within the framework of nonlinear quantum mechanics. After discussing statistical and experimental information regarding Bose-Einstein condensation, as well the characteristics of nonlinear equations and the Mean-Field Theory that best describes bosonic systems, Bose-Einstein condensation is defined by the nonlinear onedimensional Gross Pitaevskii equation. Initially, the Gross Pitaevskii equation is explored when the trap potential is zero, and later under the Pöschl-Teller potential, which holds significant importance in quantum mechanics. Two different methods are used to solve the Gross Pitaevskii equation: the Homotopy Perturbation method and the Bernoulli Sub-equation Function method. The efficiency and accuracy of both methods are analyzed and compared.</p>