Another Notation Thing: Del^2 V

  • Thread starter Swapnil
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  • #1
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Main Question or Discussion Point

What does the subscript [tex](\theta, \phi)[/tex] mean on the laplace operator? i.e.

[tex]{\nabla}^2 V_{(\theta, \phi)}[/tex]
 

Answers and Replies

  • #2
robphy
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Can you provide the context of this notation?
 
  • #3
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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
 
  • #4
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I think the variables should be on the operator, and not on the potential. I've seen it most commonly like this:

[tex]\nabla^2_{r'} V(r-r')[/tex]

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)
 
  • #5
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I think the variables should be on the operator, and not on the potential. I've seen it most commonly like this:

[tex]\nabla^2_{r'} V(r-r')[/tex]

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..:blushing: I meant to put the subscript on the operator not on the function. Sorry about that.
 
  • #6
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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 [tex]{{\nabla}^2}_{(\theta, \phi)} V[/tex] is used to denote the variables which are held constant while the notation [tex]{{\nabla}^2}_r V[/tex] is used to denote the variable(s) which are being integrated over.
 
  • #7
quasar987
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I've seen [tex]\nabla^2_{xy}[/tex] to mean

[tex]\nabla^2_{xy}=\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}[/tex]
 
  • #8
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I've seen [tex]\nabla^2_{xy}[/tex] to mean

[tex]\nabla^2_{xy}=\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}[/tex]
This is what i would say. i believe the theta and phi in the subscript in the original post imply spherical coordinates.
 
  • #9
Meir Achuz
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without the radial derivatives.
 

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