Hi, lately I've been messing around a lot with the Laplacian operator and DE's including the Laplacian operator. Most recently, the equation below is the one I have been messing around with and trying to understand better.(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\nabla^2 U(\vec{r})=C(\vec{r})U(\vec{r})[/itex]

This is pretty general though.. WAYY too general for me to tackle. So I've been starting with the 1D case, which I also can't seem to solve.

[itex]\frac{d^2}{dx^2}U(x)=C(x)U(x)[/itex]

My goal is to try to solve for U(x) in terms of C(x). Any ideas? Is there any way to know if such a solution exists? What about to the general equation above?

Thanks :)

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# Curious About this DE

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