In equation (1.38) the discrete summation over momenta in a
volume should be replaced by integration over
. The result is
(1.39)
The first term of this expression gives the mean-field energy and
coincides with the result obtained from the Gross-Pitaevskii
equation (1.14). The second term gives the correction to the
ground state energy arising from the zero-point motion of the quasiparticles
(1.40)
The result is valid if the system is dilute, i.e. if the gas
parameter is small .