Proving Equality around r=0: Tips and Hints

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SUMMARY

The discussion focuses on proving an equality that holds for all points outside a small region around r=0, where both sides of the equality equal zero. The main challenge lies in demonstrating the equality in the vicinity of r=0. Participants suggest using spherical coordinates to integrate over a region that includes r=0 as a potential approach to tackle this problem.

PREREQUISITES
  • Understanding of spherical coordinates in calculus
  • Familiarity with limits and continuity in mathematical analysis
  • Knowledge of integration techniques
  • Basic concepts of mathematical proofs
NEXT STEPS
  • Research integration techniques in spherical coordinates
  • Study limits and continuity around singular points
  • Explore methods for proving mathematical equalities
  • Review examples of mathematical proofs involving r=0
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Mathematicians, physics students, and anyone involved in advanced calculus or mathematical proofs, particularly those dealing with singularities and integration techniques.

wormhole
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i want to prove this equality:

dirac_lap.jpg


it is trivial to show that it holds for all points outside small certain region around r=0
in this case both sides of equality are 0

i have a dificulty in proving the equality in region r~0

so please give some hint how to attack this thing...:smile:
 
Last edited:
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Integrate over a region containing r=0 using spherical coordinates
 

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