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New in Mathematica 9Parametric Differential Equations

Eigenproblems 

Find an eigenfunction for the finite square well eigenproblem , , , where is a square well potential of height 5.

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Start by plotting solutions of for .

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The true eigenfunctions satisfy . These can be approximated by finding functions with . Because the equation is symmetric in , only solutions with need to be found. Plot for .

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The root is the approximate eigenvalue.

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Plot the approximate eigenfunction together with solutions for nearby .

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