# On 2D Inverse Problems/Schrodinger equation

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The **conductivity equation**

can be rewritten as the **Schrodinger equation**

where,

For the analog of this system to work on networks, one can define the solution of the Schrodinger equation *u* on the nodes and the square of the solution on the edges by the following formula:

**Exercise (*).**Express the Dirichlet-to-Neumann operator for the Schrodinger equation in terms of the Dirichlet-to-Neumann operator for the corresponding Laplace equation on the network with the same underlying graph.

(Hint). Let

where,

Then

is the Laplace matrix of the network with

w/

and

**Exercise (**).**Reduce the inverse problem for Schrodinger operator to the inverse problem for the Laplace operator on the network w/same underlying graph (w/ possibly signed conductivity).