# Another Notation Thing: Del^2 V

What does the subscript $$(\theta, \phi)$$ mean on the laplace operator? i.e.

$${\nabla}^2 V_{(\theta, \phi)}$$

robphy
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Gold Member
Can you provide the context of this notation?

hmm, the lapace operator is normally just the nabla^2, perhaps the subscipt specifies the variables/co-ordinates of the function V on which the laplace operator is operating

I think the variables should be on the operator, and not on the potential. I've seen it most commonly like this:

$$\nabla^2_{r'} V(r-r')$$

where the subscript is to remind us that, as CPL.Luke says, that we are differentiating with respect to the dashed variables (or undashed, as it is in your example)

I think the variables should be on the operator, and not on the potential. I've seen it most commonly like this:

$$\nabla^2_{r'} V(r-r')$$

where the subscript is to remind us that, as CPL.Luke says, that we are differentiating with respect to the dashed variables (or undashed, as it is in your example)
Ooops.. I meant to put the subscript on the operator not on the function. Sorry about that.

In response to the context of my question, the author who used this notation was integrating the potential on the surface of the sphere. So I guess the notation $${{\nabla}^2}_{(\theta, \phi)} V$$ is used to denote the variables which are held constant while the notation $${{\nabla}^2}_r V$$ is used to denote the variable(s) which are being integrated over.

quasar987
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Gold Member
I've seen $$\nabla^2_{xy}$$ to mean

$$\nabla^2_{xy}=\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}$$

I've seen $$\nabla^2_{xy}$$ to mean

$$\nabla^2_{xy}=\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}$$

This is what i would say. i believe the theta and phi in the subscript in the original post imply spherical coordinates.

Meir Achuz