關於二維逆問題/薛定諤方程

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).

練習 (**)。將域上的薛定諤方程的逆問題簡化為電導率 c 的電導率方程。