 a harmonic trap).The time-independent Gross–Pitaevskii equation, for a conserved number of particles, is

where formula_24 is the chemical potential.The chemical potential is found from the condition that the number of particles is related to the wavefunction by

From the time-independent Gross–Pitaevskii equation, we can find the structure of a Bose–Einstein condensate in various external potentials (e.g.