- #1
Replusz
- 142
- 14
- TL;DR Summary
- 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!
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Changing to Polar coordinates in order to calculate this integral
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- Thread starter Replusz
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In summary, polar coordinates are a way of representing points in a two-dimensional space using a distance from the origin and an angle from a reference line. They can be used to solve integrals involving circular or rotational symmetry, where they may be more efficient than traditional rectangular coordinates. To convert from rectangular coordinates to polar coordinates, one can use the equations r = √(x² + y²) and θ = tan^-1(y/x). However, polar coordinates may not be suitable for all types of integrals and can sometimes add complexity to the solution. It is important to consider both rectangular and polar coordinates when approaching an integration problem.
- #2
Gaussian97
Homework Helper
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Try to write 3.66 in spherical coordinates, and perform the integrals of ##\phi## and ##\theta##.
- #3
Replusz
- 142
- 14
I get a part where I have to integrate (cos(kr*cos(theta))+i*sin(kr*cos(theta)))*sin(theta) dtheta
Which seems terrible
Which seems terrible
Last edited:
- #4
Replusz
- 142
- 14
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! :)
(imaginary part is 0, real part gives 3.67)
Thank you Gaussian97! :)
1. How do I convert an integral from Cartesian coordinates to Polar coordinates?
To convert an integral from Cartesian coordinates to Polar coordinates, you can use the following transformations:
x = r cos(theta) and y = r sin(theta). This will change the limits of integration and the integrand, which will then allow you to use the appropriate formulas for integration in Polar coordinates.
2. What is the benefit of using Polar coordinates to calculate an integral?
Using Polar coordinates can simplify the calculation of certain integrals, particularly those involving circular or symmetric regions. It can also provide a more intuitive understanding of the geometric interpretation of the integral.
3. How do I determine the new limits of integration when converting to Polar coordinates?
The new limits of integration in Polar coordinates will depend on the shape of the region being integrated over. Generally, the limits will be determined by the intersection points of the curve or shape in the Cartesian coordinates and the lines theta = a and theta = b in the Polar coordinates.
4. Can I use Polar coordinates for any type of integral?
No, Polar coordinates are only applicable for certain types of integrals, specifically those involving circular or symmetric regions. For other types of integrals, it may be more appropriate to use Cartesian coordinates or other coordinate systems.
5. How do I know when to use Polar coordinates instead of Cartesian coordinates for an integral?
You can use Polar coordinates when the region being integrated over has circular or symmetric properties. This can be determined by examining the equation of the curve or shape and identifying any circular or symmetric patterns. Additionally, if the integrand contains terms involving r or theta, it may be more appropriate to use Polar coordinates.
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