Classical description of a particle in a sphere...

[DeanK2]

I would like to set up a statistcal equation to describe the probabiliity of where a particle can be found in a sphere of zero potential, and the collisions betweeen the wall and particle is perefctly elastic.

[swansont]

If the sphere is rigid, wouldn't this just be a constant?

[granpa]

you would need to introduce some randomness. it could just go back and forth along one line through the center.

 

I very much doubt that the electron probability cloud has such a distribution. if thats what you are thinking then my advice woud be not to bother.

[Severian]

A more interesting question would be to do it quantum mechanically. Set V=0 in the sphere and V infinite outside the sphere, and then enforce Schrodinger's Equation on the wavefunction. Off the top of my head, the angular distribution will be spherical harmonics, while the radial equation is just like the 1-dimensional infinite square well, but with a centrifugal barrier (which depends on the angular momentum of the particular harmonic).

[DeanK2]

I have done the particle in a sphere with QM, but am trying to contrast it with the classical description.