Quantum Mechanics Equation Question

[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?

 

[dextercioby]

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

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

 

[cpt_carrot]

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

 

[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.

 

[atomicpedals]

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