Forgive me if I'm just having a mental block about this, but I'm teaching myself the sturm-liouville method - I'm happy with getting the general ODE to this (self-adjoint) form after adjusting for any weighting function):(adsbygoogle = window.adsbygoogle || []).push({});

$$ \mathcal{L}y=\lambda y $$ the operator is of the form $$\mathcal{L}= (p(x) \frac{d}{dx})'+q(x)$$ p, q real polynomials.

None of the material I have read, or examples, show what the next step toward a solution is; examples just claim some solution and go on to discuss things like hermitian operator properties. I don't know where they get either the eigenvalues or eigenvectors from, could someone please give me a hint?

I could go back to the general linear homogeneous 2nd order ODE form and use something like Frobenius to solve that, but then what would have been the point of getting it into the S-L form?

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# Solving sturm-liouville equations

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