Talk-Polywell.org

Using the quantum model of the atom for a first approximation of thermalization in a polywell?

I'm curious whether extending the orthogonal orbitals of electrons around a nucleus as the number of electrons approaches infinity might give a useful - or at least interesting - approximation of the average radial vs axi energy of an orbital, which could at least give one new ways to look at a polywell.

The solutions to the Schodinger equation are spherical harmonics, that are not unique to quantum mechanics and have been known for a long time before that even. You can think of them just as any other complete orthogonal basis like fourier series or the cylindrical version. I'm not sure how they would give a new insight for a polywell though. What are you thinking in particular?

pretend the polywell is an atom, except it's very very large - as in extremely large. like orbitals spanning out to a meter from the nucleus. also, swap the particles - the nucleus is made up of electrons, and the orbitals are made up of ions.

that's your first approximation of a model of a polywell.

now, you can find the probability-weighted averages of the radial velocities, or the axial velocities, or the energies... (bearing in mind since there are some things you wont be able to solve for simultaneously, ala heisenberg).

or you can add in a fusion probability kernel to the equation.

etc.

The ion distribution is solving the boltzmann equation. So, you'd have to show that you're getting a solution to that, instead of the schrodinger equation.

you're saying because it follows bose-einstein statistics? or because the mass-charge ratio is 8000x as much, the differerence byetween quantum and classical is that much smaller, presumably?

http://en.wikipedia.org/wiki/Boltzmann_equation

It's the general equation for the particle distributions. This is in the classical mechanics realm.

came up with it in ... 1872 ... what a showoff!

a think i saw that equation on a "what part of ... don't you understand?" shirt.

Yes, it truly does bring to mind "If I have seen further it is by standing on the shoulders of Giants"