Changing to Polar coordinates in order to calculate this integral

Click For Summary

Discussion Overview

The discussion revolves around the process of changing to polar coordinates to calculate a specific integral. Participants explore the implications of this transformation in the context of spherical coordinates and the associated integrals.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant suggests writing a specific value (3.66) in spherical coordinates and performing the integrals of the angles φ and θ.
  • Another participant expresses difficulty with an integral involving trigonometric functions and complex exponentials, indicating it is challenging to solve.
  • A later reply mentions using WolframAlpha to verify the approach, concluding that the imaginary part of the integral is zero and the real part yields a value of 3.67.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the ease or difficulty of the integral, and there are differing views on the verification of the results obtained.

Contextual Notes

The discussion includes assumptions about the transformations and the specific integral being evaluated, but these assumptions are not fully articulated or resolved.

Replusz
Messages
141
Reaction score
14
TL;DR
I am a bit lost regarding what happens here.
the k^2+m^2 part stays there.
What happens to the exp? and to the d^3k ?

Thank you!
1586771830443.png
m a
 
Last edited by a moderator:
Physics news on Phys.org
Try to write 3.66 in spherical coordinates, and perform the integrals of ##\phi## and ##\theta##.
 
  • Like
Likes   Reactions: Replusz
I get a part where I have to integrate (cos(kr*cos(theta))+i*sin(kr*cos(theta)))*sin(theta) dtheta
Which seems terrible
 
Last edited:
OK with the help of wolframalpha I convinced myself that this is indeed what we want.
(imaginary part is 0, real part gives 3.67)

Thank you Gaussian97! :)
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 10 ·
Replies
10
Views
4K
  • · Replies 4 ·
Replies
4
Views
2K