On 2D Inverse Problems/Schrodinger equation

The conductivity equation ${\mathrm{\Delta }}_{\gamma }u=\mathrm{\nabla }\cdot (\gamma \mathrm{\nabla }u)=0$ 

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

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

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: <math>\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.