Methods for a Nonuniform Bose Gas.
We review mathematical methods for the treatment of a system of Bose particles with nonuniform density. The use of the pseudopotential is explained, especially with respect to negative scattering lengths. It is emphasized that the delta-function potential produces no scattering in three dimensions, and should not be used in the Bogoliubov self-consistent field method, which is variational in nature. A common misuse of the Bogoliubov method at finite temperatures is pointed out. A Gaussian variational method is proposed.
Center for Theoretical Physics, Laboratory for Nuclear Science, and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139.
Kerson
K
Huang
Institute for Theoretical Atomic and Molecular Physics, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138.
Paolo
P
Tommasini
Bogoliubov transformation; Bose gas; Bose-Einstein condensation; Gaussian wave function; hard-sphere interaction; negative scattering length; pseudopotential; self-consistent field; variational method