Quantum Mechanics Equation Question

1. Aug 9, 2011

atomicpedals

I'm typing up my notes and I came across the attached equation and it seems I didn't write anything else about it; so, does it have a name or special classification?

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2. Aug 9, 2011

dextercioby

It's no equation, it's an equality written incorrectly, because

$$\frac{1}{r} \frac{\partial^2}{\partial r^2} r = 0$$

3. Aug 9, 2011

cpt_carrot

But it's fine as an operator equality
$$\frac{1}{r}\frac{\partial^2r\psi}{\partial r^2}=\frac{\partial^2\psi}{\partial r^2}+\frac{2}{r}\frac{\partial\psi}{\partial r}$$

Last edited: Aug 9, 2011
4. Aug 9, 2011

Herr Malus

If I remember correctly, this is the Laplacian in 2D, with azimuthal symmetry.

Edit: No, I'm wrong. Perhaps it has something to do with the 3D wave equation. I definitely saw this in a PDE course.

Last edited: Aug 9, 2011
5. Aug 9, 2011

atomicpedals

Operator equality and 3D wave equation both definitely fit with where it is in my notes!