Quantum Corrals A Finite Element Analysis

From the standpoint of the Schrodinger equation, this is another example of a particle in a box problem which in this case is effectively two-dimensional. In particular, the potential within the corral region is assumed to be zero, while the 

As a result of our separation of variables strategy, the problem of solving the Schrodinger equation for the quantum corral is reduced to that of solving two ordinary differential equations. In particular, we have 

The r equation can be massaged into the form of a Bessel equation while the 9 equation is elementary. As a result of these insights, the solution may be written as Jn s/2mE jh. It now remains to impose our boundary conditions. We 

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