# 2 electrons in box, hard walls, total energy E.

1. Apr 16, 2010

### Spinnor

2 electrons in box, "hard" walls, total energy E.

Say we place 2 electrons inside an empty 1m cubed box with very "hard" walls, the electrons can penetrate only a very small distance into the walls of the box. Let us say that any photons produced by the scattering of the two electrons stay in the box as the box walls perfectly reflect them.

Could such a setup be envisioned in theory?

Say we start out such that the total energy in the box is above the rest energy of the two electrons and large enough such that photons from electron scattering have a wavelength much smaller then the size of the box. Now let billions of years pass.

In time the electrons will scatter and produce real photons?

Let enough time pass such that the 2 electrons come into equilibrium with the electromagnetic field, does theory allow me to divide the total energy inside the box into a sum of two parts, the energy of the 2 electrons and the energy in the electromagnetic field (I'm guessing one might also like to account for the energy in the field of the positron)?

As the total energy of the contents of the box gets to be hundreds or billions of times the rest mass of an electron can one make a hand waving argument as to how the energy in the box gets divided between the 2 electrons and the electromagnetic field (and all known fields)?

Thanks for any help!

2. Apr 16, 2010

### LostConjugate

Re: 2 electrons in box, "hard" walls, total energy E.

I do not know the answer to your primary question. You would just need to calculate the EM field based on electron scattering equations I suppose.

However this setup can not be envisioned in theory.

In order for the electron to only penetrate a very small distance the walls would need to have an infinite potential at some point. Electrons can penetrate any physical object.

3. Apr 18, 2010

### Spinnor

Re: 2 electrons in box, "hard" walls, total energy E.

Maybe I need a new box, say one from Feynman, so that my question can be considered? From page 3 of Feynman's Quantum Electrodynamics,

Chapter 1 Interaction of Light with matter-Quantum Electrodynamics

... Suppose all the atoms of the universe are in a box. ...

... The box is considered to be full of photons. ...

Change that to two electrons in the universe.

Thanks for any help!