We verify Bogoliubov’s approximation for translation-invariant Bose gases
in the mean field regime, i.e., we prove that the ground state energy
is given by
, where
is the number of
particles,
is the minimal
Hartree energy and
is the Bogoliubov Hamiltonian. As an intermediate result we show the existence of approximate
ground states
, i.e.,
states satisfying
,
exhibiting complete Bose–Einstein condensation with respect to one of the Hartree
minimizers.