Is the Dirac Delta Function Defined at Zero or Infinity?

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Homework Help Overview

The discussion revolves around the Dirac delta function and its properties, particularly concerning its definition at specific points such as zero or infinity. Participants are exploring the implications of function values and their relation to the delta function concept.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are questioning the assumptions made regarding the value of functions at certain points and their implications for defining the delta function. There is an exploration of applying the divergence theorem to understand the concept of charge distribution related to the delta function.

Discussion Status

The discussion is active, with participants offering insights into the mathematical reasoning behind the delta function. Some guidance has been provided regarding the application of the divergence theorem and the significance of certain constants, such as 4π, in the context of spherical coordinates.

Contextual Notes

There appears to be some confusion regarding the interpretation of function values at specific points and their relevance to the delta function definition. Participants are also grappling with the mathematical underpinnings of the concepts being discussed.

yungman
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I cannot get the answer as from the solution manuel.

2vl5jd0.jpg


Please tell me what am I assuming wrong.
Thanks
 
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Just showing that the value of a function is '-infinity' at a point and zero otherwise doesn't tell you it's a delta function. Apply the divergence theorem to grad(1/r) on a sphere around the origin to figure out how much 'charge' is there.
 
Dick said:
Just showing that the value of a function is '-infinity' at a point and zero otherwise doesn't tell you it's a delta function. Apply the divergence theorem to grad(1/r) on a sphere around the origin to figure out how much 'charge' is there.

I understand that and I showed in my own answer. What I don't get is where the 4[tex]\pi[/tex] come from!
Thanks
 
No, all your answer said was the value at zero is '-infinity' (I'm putting that in quotes because I'm not even sure it makes sense). I said that DOESN'T mean it's a delta function. The 4*pi comes from checking the flux through a sphere around the origin. It comes from the 4*pi in the formula for the area of a sphere.
 

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