What is the self energy of electrons and how can it be calculated accurately?

In summary, the self energy of electrons is the potential energy that an electron exerts on itself. It arises from the interaction of an electron's charge with its own electric field. This self energy can be calculated accurately using the quantum mechanical theory of electron self-energy, which takes into account factors such as the electron's mass, charge, and spin. This calculation is essential for understanding the behavior and properties of electrons in various physical systems.
  • #1
microtopian
5
0
The following two questions regard the self energy of electrons.. Does anybody know how to start these? I used this site as reference but I wasn't sure if they help with these following questions: http://quantummechanics.ucsd.edu/ph...tes/node44.html

Calculation 1: Pretend the electron is made up of two halves, each with charge e/2. How much energy is required to bring the two halves together, i.e., so that they occupy the same point in space?

Calculation 2: That calculation was a bit over-simplified. Let’s do a better job. Pretend that the charge of an electron is spread uniformly over the surface of a spherical shell with radius r0. Next calculate the electric field everywhere in space, i.e., at an arbitrary distance r from the center of the shell. Obviously the answer will depend on r and r0. Next, calculate the total energy stored in the field, by integrating the energy density u over all space. Finally, let the “electron” become a point particle, by letting r0 go to zero.
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
If you're you taking the electron to be a point particle, you won't get a finite answer using classical methods. QED resolves this paradox.
 
Last edited:
  • #3
Assume that you're calculating/observing the energy from the zero momentum frame. You then calculate the energy of the particle's bare mass (the mass that would be there if no charge was present) and then calculate the electrons mass-energy from the expression for energy density of the E-field. The divide the energy by c^2.

When you take the limit r-> 0 you'll get an infinite amount for the energy.

Pete
 
  • #4
Any graduate level text (Jackson, Panofsky and Phillips) will discuss the self energy problem. Your approaches are not unreasonable, and the last is more-or-less standard in the literature. But the plain fact remains, that in the limit of a point particle, the answer for the energy is infinite. This is true in QED as well. We're talking an unsolved and vexing problem.

Regards,
Reilly Atkinson
 

1. What is the concept of self energy of electrons?

The self energy of electrons refers to the energy that an electron possesses due to its own electric field. This energy arises from the interaction of the electron with itself, and it contributes to the total energy of the electron.

2. How is the self energy of electrons calculated?

The self energy of electrons can be calculated using the classical formula for electric potential energy: U = kq2/r, where k is the Coulomb constant, q is the charge of the electron, and r is the distance between the electron and itself. This calculation can also be done using quantum mechanics and the concept of electron wavefunctions.

3. Does the self energy of electrons affect their behavior?

Yes, the self energy of electrons plays a role in determining the behavior of electrons in an atom or molecule. It contributes to the overall energy of the electron, which affects its movement and interactions with other particles.

4. Is the self energy of electrons a constant value?

No, the self energy of electrons can vary depending on the environment and the interactions of the electron with other particles. It also depends on the distance between the electron and itself, which can change as the electron moves within an atom or molecule.

5. How does the self energy of electrons relate to the concept of electron shells?

The self energy of electrons contributes to the overall energy level of an electron, which is a factor in determining the electron's placement in an atom's electron shells. The higher the self energy, the more energy the electron has and therefore the higher its energy level and shell placement.

Similar threads

Calculating the force on an electron from two positive point charges
    • Electromagnetism
Replies
2
Views
754
I Potential Energy of an Electron-Nuclei Interaction in DFT
    • Quantum Physics
Replies
1
Views
704
What happens to an electron in a magnetic field?
    • Electromagnetism
Replies
8
Views
1K
I The electron as a smeared charge density
    • Quantum Physics
Replies
13
Views
2K
Why doesn't an electron lose energy between components?
    • Electromagnetism
Replies
7
Views
2K
A Renormalization (Electron self energy)
    • Quantum Physics
Replies
4
Views
2K
Electromotive Force, Batteries, Resistors, and Potential Differences
    • Electromagnetism
Replies
17
Views
1K
How do we know the mass of an electron?
    • Electromagnetism
Replies
28
Views
2K
I An attempt to understand the associated variable conventions in circuits
    • Electromagnetism
Replies
1
Views
825
A Understanding & Solving Electron/Phonon Interaction Problems
    • Atomic and Condensed Matter
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top