= Gross–Pitaevskii equation
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{title2=$i\hbar\partial_t\psi=(-\hbar^2\nabla^2/(2m)+g|\psi|^2+V)\psi$}
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= GPE
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{synonym}
The <Gross–Pitaevskii equation> describes a dilute interacting condensate through a complex <order parameter> $\psi$, normalized so that $|\psi|^2$ is <number density>. Repulsive contact interactions have $g>0$. In a frame rotating at the condensate frequency, the operator includes $-\mu$, with <chemical potential> $\mu$. It is generated by a <Hamiltonian> <functional>; its homogeneous positive-density state has $n_0=\mu/g$ when $g,\mu>0$.
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