Wolfram then has the atomic orbitals solved

Right here at their link for Lagrange numbers.

Lagrange numbers are of the form

(2)

where is a Markov number. The Lagrange numbers form a spectrum called the Lagrange spectrum.
Given a Pell equation (a quadratic Diophantine equation)

(3)

with a quadratic surd, define

(4)

for each solution with . The numbers are then known as Lagrange numbers (Dörrie 1965). The product and quotient of two Lagrange numbers are also Lagrange numbers. Furthermore, every Lagrange number is a power of the smallest Lagrange number with an integer exponent.

The hyperbola formula, taken from either the top or from the Pell gives an equation of a hyperbola. The asymptote from wiki:

 This is simply the allowable error, and the b has the Markov number.


The electron has to minimize the error along the radial axis to the center of the proton, and simultaneously minimize the error tangent to its surface.  Hence, the variance of the error, e, above, the eccentricity, has two differential solutions along the two axis, and we get two solutions for the first atomic orbial.

We raise the spectral mode by raising the Markov number.  But you can see that the Lagrange numbers are powers. so we have the second error functions looks like:

 e+e^2, a series of two powers.  We square that and take the derivatives along two lines of symmetery and we get six solutions.

Wash rinse and repeat, do a better job than my handwaving.

The first hyperbola is an extremely narrow hyperbola, its inverse nearly verticle.  It is going to be a sphere, two spheres with two solutions.  Adding the third Markov, moves the first set of solutions relative to the new line of symmetry.

Your uncertainty is simply the smallest number of items that Higgs can handle, mainly, 2^17  - 1, and that is the base Gaussian 'baud' in a channel. 

The q in the equation to the left is uncertain, and feel free to scale  it.  You end up with this simple Gaussian channel with three degrees of freedom when all is said and done. Adding energy powers up and adds solution. You will find all the existing polynomials Schrodinger used by following the links to perfect numbers, Mersenne primes, and Markov. The electron is simply maintaining the value of the finite log, keeping a yardstick. The engineering approximations were unitized down to tiny things that need counting.

What about wave number shift and phase gradients?

Compute the solutions and apply the shifts after the fact.Or just forget about it, after all the Markov numbers were a result of the shifts.

So I suggest we give the Nobel to whomever wrote up that note in Wolfram on Lagrange and the mathematicians at Wiki who did Markov, number theory, Zeta  and entropy..