Friday, July 24, 2015

Magic Numbers, Get Them Here!

With the light speed limit, the orbiting particles cannot be at greater speed.  When the particle is at light speed, depending on \(x_z\) there are limited number of possible valid orbits,


 When \(x_z\) is small, only one of the Quantum Wells is available for occupancy.  It is possible that only the solution of higher \(x\) are possible, the other being too close to the containing particle.  If this is so,  only two particles are in orbit.  Otherwise there are four particles.

It is likely that, as in the case of the hydrogen atom, only the two higher orbit can be occupied, the lower orbits being too close to the nucleus.

As \(x_z\) get greater,


and greater,


These are single centered \(\psi\) clouds.  Apart from being a container for magic numbers, non sequitur.