Abstract
In this work I solve the Gross-Pitaevskii equation describing an atomic gas confined in an isotropic harmonic trap by introducing a variational wavefunction of Gaussian type. The chemical potential of the system is calculated and the solutions are discussed in the weakly and strongly interacting regimes. For the attractive system with negative scattering length the maximum number of atoms that can be put in the condensate without collapse begins is calculated.
Highlights
Bose-Einstein condensation (Pethick & Smith, 2008) is the macroscopic occupation of the lowest momentum state with a finite fraction of particles
In this work I solve the Gross-Pitaevskii equation describing an atomic gas confined in an isotropic harmonic trap by introducing a variational wavefunction of Gaussian type
We make an appropriate ansatz of a trial variational wavefunction of Gaussian type which will be followed by the calculation of the ground state energy which consists of three parts
Summary
Bose-Einstein condensation (Pethick & Smith, 2008) is the macroscopic occupation of the lowest momentum state with a finite fraction of particles. Different theoretical approaches have been used to study these systems that undergoes Bose-Einstein condensation. These methods include mean-field theories (Margetis, 2015), canonical and microcanonical ensemble approaches (Chase, Mekjian, & Zamick, 1999), and numerical calculations including quantum Monte-Carlo techniques (DuBois & Glyde, 2001). These systems are weakly-interacting ultracold atomic gases confined in an external trap. We make an appropriate ansatz of a trial variational wavefunction of Gaussian type which will be followed by the calculation of the ground state energy which consists of three parts
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