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: <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.