= Spatial phase gradient of a Schrodinger wavefunction
{title2=$\mathbf j=\rho\hbar\nabla\theta/m$}
Where a nonzero <wavefunction> can be written as $\psi=\sqrt\rho e^{i\theta}$, and there is no <vector potential>, substituting into the Schrodinger <probability current> gives $\mathbf j=\rho\hbar\nabla\theta/m$. The direction of <probability> flow is determined by the <phase> gradient rather than the slope of the <real part>. A <plane wave> and its <complex conjugate> have the same <real part> and density but opposite currents. In a <vector potential> the gauge-invariant kinetic <momentum> replaces $\hbar\nabla\theta$.
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