Electrons on a ring - too easy.

[Fallen Seraph]

Homework Statement

Three electrons are confined to move on a ring of radius R. Find the equilibrium positions of the electrons in terms of the angles between them.

Homework Equations

Some hints with differentials are given to us, as is the potential between two of the electrons , but as far as I can tell these are completely redundant.

The Attempt at a Solution

Well my problem is this: we've been given this question in a second year comp lab and the answer is so glaringly obvious to me that I can only come to the conclusion that I'm misunderstanding something. I don't get how one could possibly need a computer to get this.

As I see it, the three electrons being identical particles implies that the final state must be symmetric under interchanging the particles. And on a ring the only way to do this is to have them all separated by 120 degrees.

Surely it can't be that simple? What am I missing?

 

[blochwave]

The answer might be obvious but computationally it's not the simplest thing in the world to prove by hand

EDIT: It's kinda like the classic prove the shortest distance between two points in a euclidean geometry is a straight line. Duh, right? So go ahead and do it

There's an INFINITE number of other possible paths to take(just like here there are infinite configurations) you're going to have a helluva time going through all infinite cases and showing they don't work