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On 2D Inverse Problems/Schrodinger equation

< On 2D Inverse Problems(Redirected from User:Daviddaved/Schrodinger equation)
The conductivity equation  
is equivalent to Schrodinger equation: 
for potential 
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: 
Exercise (*). Express the DN operator for the Schrodinger equation in terms of the one for the conductivity equation on the same e-network.

(Hint). Let



is the Laplace matrix of the network.

Exercise (**). Reduce the inverse problem for the Schrodinger equation on e-nerwork to the conductivity equation one w/signed conductivity.