hello sir,ChrisVer said:1st step: go to "spherical coordinates" and integrating out the [itex]\phi[/itex]... [itex] u = \cos \theta [/itex]
2nd step: Integrating wrt to [itex]u[/itex], will give a difference of [itex]e^{i~something} - e^{-i~something} \propto \sin (something) [/itex]. In fact I wouldn't ever write it in terms of sin...
3rd step: uses that he has two integrals one with the exponential with + and the other with the exponential with - ... then changes the integration variable of the one from k to -k, and gets this result.
4th step: factorizes the denominator.
5th step and then final: solves the (complex) integral
If you want to see a step in more details, you can ask for a specific one.
Muh. Fauzi M. said:i can't get the 3rd step. is change the integration variable, change the value from k to -k in that term, including the dk -> d(-k)?
The Yukawa Potential, also known as the screened Coulomb potential, is a mathematical expression that describes the interaction between two charged particles in quantum field theory.
The Yukawa Potential was first derived by Japanese physicist Hideki Yukawa in 1935 as a modification to the traditional Coulomb potential to account for the effects of quantum field theory.
The Yukawa Potential is derived by considering the exchange of virtual particles between two charged particles. This exchange creates an attractive or repulsive force, depending on the charges and distances between the particles.
The Yukawa Potential is significant because it provides a more accurate description of the interaction between particles at short distances, such as within atomic nuclei, where the traditional Coulomb potential breaks down.
The Yukawa Potential has applications in various fields, such as nuclear physics, particle physics, and astrophysics. It is used to explain the forces between particles and the structure of atomic nuclei. It also plays a role in the study of dark matter and the behavior of neutron stars.