  The Gross-Pitaevskii equation is discussed at the level of an advanced course
on statistical physics. In the standard literature the Gross-Pitaevskii
equation is usually obtained in the framework of the second quantisation
formalism, which in many cases goes beyond the material covered in many
advanced undergraduate courses. In this paper, we motivate the derivation of
the Gross-Pitaevskii equation (GPE) in relationship to concepts from
statistical physics, highlighting a number of applications from dynamics of a
Bose-Einstein condensate to the excitations of the gas cloud. This paper may be
helpful not only in encouraging the discussion of modern developments in a
statistical mechanics course, but also can be of use in other contexts such as
mathematical physics and modelling. The paper is suitable for undergraduate and
graduate students, as well as general physicists.
