# On 2D Inverse Problems/Schrodinger equation

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

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

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

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: [itex]\c^2(a,b) = x(a)x(b).