Gross–Pitaevskii equation

The Gross–Pitaevskii equation (GPE, named after Eugene P. Gross and Lev Petrovich Pitaevskii ) describes the ground state of a quantum system of identical bosons using the Hartree–Fock approximation and the pseudopotential interaction model.

In the Hartree–Fock approximation the total wave-function ${\displaystyle \Psi }$ of the system of ${\displaystyle N}$ bosons is taken as a product of single-particle functions ${\displaystyle \psi }$,

where ${\displaystyle \mathbf {r} _{i}}$ is the coordinate of the ${\displaystyle i}$-th boson.

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