Fizika Nizkikh Temperatur: Volume 44, Number 11 (November 2018), p. 1549-1553 ( to contents , go back )
On the ground state energy for a finite inhomogeneous degenerate Bose gas
V.B. Bobrov1,2, A.G. Zagorodny3, and S.A. Trigger1
1Joint Institute for High Temperatures, Russian Academy of Sciences,Izhorskaya St. 13, Bd. 2, Moscow 125412, Russia
2National Research University “Moscow Power Engineering Institute”,Krasnokazarmennaya 14, Moscow,
3Boholyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine 14-b Metrolohichna Str., Kiev 03680, Ukraine
Received May 14, 2018, revised Jule 3, 2018, published online September 26, 2018
Within the framework of the self-consistent Hartree–Fock approximation, the ground state energy for a finite inhomogeneous system of bosons located in a scalar external field was found on the basis of the second quantization representation without using the formalism of anomalous averages. The wave function of the ground state corresponds to the stationary Gross–Pitaevskii equation for the wave function of the Bose–Einstein condensate. It is shown that the ground state energy can be found from the energy determined from the stationary Gross–Pitaevsky equation only for a system that satisfies the thermodynamic limit.
Key words: ground state energy, inhomogeneous Bose–Einstein condensate, self-consistent Hartree–Fock approximation.