2013/07/15 by George Rawitscher, Rawitscher, George
Physics and Astronomy · #Atomic Physics (physics.atom-ph) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum, superfluid, helium dynamics
paper · pdf · doi:10.48550/arxiv.1307.4031
openalex publication_date 2013/07/15 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
The Gross-Pitaevskii equation (GP), that describes the wave function of a\nnumber of coherent Bose particles contained in a trap, contains the cube of the\nnormalized wave function, times a factor proportional to the number of coherent\natoms. The square of the wave function, times the above mentioned factor, is\ndefined as the Hartree potential. A method implemented here for the numerical\nsolution of the GP equation consists in obtaining the Hartree potential\niteratively, starting with the Thomas Fermi approximation to this potential.\nThe energy eigenvalues and the corresponding wave functions for each successive\npotential are obtained by a method described previously. After approximately 35\niterations a stability of eight significant figures for the energy eigenvalues\nis obtained.This method has the advantage of being physically intuitive, and\ncould be extended to the calculation of a shell-model potential in nuclear\nphysics, once the Pauli exclusion principle is allowed for.\n