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I have problem I wish to solve, and I wonder if anyone already delt with it when solving the schrodinger 2D equation.

say E(x,y) is a scalar field function that complies with

( [tex]\frac{d}{dx}[/tex]

^{2}+[tex]\frac{d}{dy}[/tex]

^{2}) *E(x,y)+k(x,y)*E(x,y)=k1*E(x,y)

where k(x,y)={k2 for x

^{2}+y

^{2}<R

^{2}and 0 otherwise}, i.e. a tube potential.

All is known but E(x,y).

I think it can be examined as a 2D schrodinger equation, even thow the eigenvalue k1 is known.

How can I get to start finding the solutions of this equation?

Can I expect to know how many are there? - one, two, many?