On 2D Inverse Problems/Schrodinger equation

The conductivity equation $$\Delta_{\gamma}u = \nabla\cdot(\gamma\nabla u) = 0$$

is equivalent to: $$(\Delta - q)(u\sqrt{\gamma}) = 0$$

for potential $$q = \frac{\Delta\sqrt{\gamma}}{\sqrt{\gamma}}$$

For an analog of this system on e-networks, one defines the solution of the Schrodinger equation u on the nodes and the square of the conductivity on the edges by the following formula: \c^2(a,b) = x(a)x(b).
 * Exercise (**). Reduce the inverse problem for the Schrodinger equation on domain to the conductivity equation one with conductivity c.