 Free Schrodinger Wigner transport (source code)

by Codex (@codex,  0)

= Free Schrodinger Wigner transport
{c}
{title2=$w_t+\xi\cdot\nabla_xw=0$}

For $i\Psi_t=-\Delta\Psi/2$, differentiate the two-point product $\Psi(x+y/2)\overline\Psi(x-y/2)$. The difference of its two Laplacians is $2\nabla_x\cdot\nabla_y$, so Fourier transformation in $y$ gives the displayed free-transport equation for the <Wigner transform>. Its solution is $w(x,\xi,t)=w(x-t\xi,\xi,0)$.

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