Classical hydrogen "molecule" - can it be stable?

[Swamp Thing]

Is it possible to have a configuration of two classical positive charges and two classical negative charges that will remain fairly stable (or at least metastable), if started off in some well-chosen initial condition?

For example, we might want to eliminate radiation by having the electrons move in an anti-coordinated figure-of-eight pattern so that their radiation fields cancel out at any distant point. Would that help to achieve a configuration that will not explode or implode right away?

 

[mitochan]

Hi.
Hydrogen molecule consists of two electrons and two protons. Say we put them on the corners of square whose length of the side is a. Coulomb energy (-1-1-1-1+1/√ 2+ 1/√ 2）e^2/a is negative so we may have a chance to pack many of them like sodium chloride crystals.

In 3D case of regular tetrahedron, Coulomb energy (-1-1-1-1+1+1）e^2/a is negative also.

 

[Swamp Thing]

I was somehow assuming that you need the electrons to be orbiting in order to get a time-averaged zero force.

It's pretty interesting that a static system could be stable.

 

[mjc123]

The Coulomb energy may be negative, but if you make the side of the square a/2 the energy will be twice as negative, a/4 four times, and so on - they will collapse onto each other, just like a static proton and electron at distance a.

 

[mitochan]

Hi.
Yea, as hydrogen atom made of positive charge proton and negative charge electron can not exist with particles apart in classical physics.