What is in those electron orbitals?

Wave(k) does not have Null(k), it has Null(k-1), it can't pack the proper quant of null.   Wave(k) has dumped excess phase into the orbital, and the Null(k-1) is now a Null(k) but half packed with phase.

So, what remains in the orbital? Up to half a quant of free Nulls. And the electron does indeed operate like a spread out bunch of nulls. I do not think is it is a probability of finding an electron, it is the actual electron is spread around. There are not enough Nulls to pack the next quant up, so add energy to that orbital, and the current quant of electrons mixes and matches with the 1/2 quant of free nulls. It really does spread around. Phase is unbalanced and held by the proton charge, phase can't fly away.  So, up to a point, those orbitals are Null soup, nothing but a mish mash of unbalanced phase and free Nulls.

This came up because I was looking at how the hyperbolics would accumulate imbalance as they march energy up the orbitals. The functions are ideal, for the purpose, they keep fractions and count out the orbitals with few operations.  I substitute the twos base for the natural log, and fractions appear to accumulate smoothly.

Anyway, I went through the Schrodinger stuff for the hydrogen atom, I took that class and I get what is happening.  But here is the thing. We know we step energy levels by Plank.  We know we are at maximum entropy. So we have to sample at twice Plank, and we have to encode the spherical charge function and mass function.  We know we are symmetric about the nucleus. So, simple enough in the bitstream version.  Energy levels count as Plank, they are the signal. Amplitude, quant size, count as log Plank.  I think your noise is actually the spheroidal functions you need to quantize. What I mean is that the spheroidal charge is a disturbance to the system, and it is resolved by quantization.

So, just plug is in and sample away. The hyperbolics should count out properly. You may have no idea what the quants mean, but they should be accurate. So give them meaning after the fact, count up first, then apply physics second. The same way I did the Plank black body. Applied force, or applied heat, or applied gravity, or whatever are disturbances to the quantum system, they should normally be noise in the Shannon equation. But the S/N is always an energy ratio. It took me a while to get that. So, we want to know the orbitals for a certain energy level. The hyperbolics count out the kinetic and potential, as you step through the Plank energies. It is just a sampled data version of the Hamiltonian.