Another Notation Thing: Del^2 V

[Swapnil]

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

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

 

[robphy]

Can you provide the context of this notation?

 

[CPL.Luke]

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

 

[masudr]

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)

 

[Swapnil]

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.

 

[Swapnil]

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]

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

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

 

[jasc15]

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]

without the radial derivatives.