On 2D Inverse Problems/Schrodinger equation
The conductivity equation
can be rewritten as the Schrodinger equation
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.
is the Laplace matrix of the network with
- 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).