Trepidation into basic quantum theory of the fusor

[quinnrisch]

This is my first gleening into the quantum workings of the fusor. I am sure that there are other mitigating factor that I am not taking into account, and I might even be wrong on the few points I am bringing up. Please feel free to correct me.
__________________________________________________________
First I will only concern myself with ONE duetron ion in a basic fusor, one anode and one cathode.

Next I will construct the two electrodes to be very close together so that the potential well approaches a STEEP wall that can be very closely aproximated by a step function. That is to so the problem looks almost like a spherical well.

Assume there is no angular momentum.

Then the wave function of the single duetron is a spherical bessel function of first order = sin(nkr)/(nkr)
The probablity of finding the duetron in any one place in the well is therefore ( sin(krn)/(krn) )^2

The energy of the various excited wave functions is given by:
E = ((h*n*pi)^2)/(8*(pi^2)*M*R^2)
where h = planck's constant; n = an interger, the excited states number; M = mass of duetron; R = radius of outer sphere

if we assume that the fusor is 2 cm in diameter then we get the voltage of the ground state of the fusor to be roughly 1 X 10^-18 Volts.
This means that our operating voltage of greater than 10kV is gigantic in comparision to the ground state and therefore the quantum number is very large. Since the quantum numbner is very large the correspondence principle is in full effect and the fusor can indeed be analyzed using classical theory.

The moving of the to electrodes further away from one another will effect things somewhat but I do beleive that it won't destroy the estimation. This estimation ises only one duetron, and therefore is insufficent to explain everything in the fusor and this model DOES NOT analyze any collisons. ( The collisions will need to be analyzed quantumly) The analysis used an infinite potential wall for simplicity sake, and doesn't hurt the overview of the analysis.
__________________________________

This was just some basics I went over this weekend that I decided to share. Any comments...