I started this project by computing (or heandwaving) the Bohr atom as a coding problem. I used mass of proton and mass of electron, computed their effective sample rate using Shannon, including the vacuum Nyquist layer.
Now we know about kinetic energy in the system from here, I can add in multiple electrons. Then add in kinetic energy, all in two steps. My approach will be to divide the volume, by radius, according to the Pauli ratio between orders. Then assign electron mass to each concentric sphere to match, compute sample rates, then lay out the quantum system as a sequence giving me the standing waves. Then I will add in kinetic energy. This is a work in progress.
Part one, using multiple atoms in the point source version (no axis of kinetic energy) is fairly simple. We know that the Pauli ratio still applies, so the region, along the radius, can be divided into Pauli wavelengths and so can the total mass of electron charge. When laid out as a sequence we will get the multiple modal standing waves.
Does the point source model account for charge interaction? Yes, when we lay out the 33% of the samples that belong to Nyquist. The standing waves we lay out are phase difference, each at its quantization range computed from relative mass ratios among the charge groups. The Nyquist are laid out so as to minimize phase along each region. Thus, the phase shift along the sequence represents a constant kinetic energy resulting from sparsity. We will decompose that phase difference along the radial and angular axis of simultaneity. Stay tuned.
We will also assume the electron speed is much less than the Pauli rate (speed of light). It is not and phycists can complain, but I am an amateur. So from the standing wave model of multiple charges in an atom, assume the longest mode is at phase zero raletive to the other charge groups. Compute the phase difference of the longest mode along the sequence and we have the force exerted from that long mode on the other charge masses. We can shift the group, except the long mode, along the plane, and remove that kinetic energy. The remaining phase variance of the group can be decomposed as the force of the next longest mode on the group. But the force from the long mode must now be decomposed in an angle to the second longest the the group. The group angle from the long and second long most is rotated a bit to make that true. Rotate the group about the line of the second longest. Each phese decomposition require one additional rotation.
Another method is the following. After breaking up you electron groups by Pauli ratio and quantizing, then break up each mode into two equal p-arts, one each for the two angles of rotation. That break kinetic energy into the three dimensions you need from the start.
What makes all of this simple is that we know the optimum congestion principle, and the Pauli rate and use relative sample rate. After that we add in the dimensional axis, we do not need to compute them along the way. That is the mistake that modern physics has been making, it is now corrected.
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