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Friday, December 15, 2017

Proton Reference

By Geek3 - Own work; created with hydrogen 1.0, CC BY-SA 3.0,

Reading over the history of the hydrogen atom and it's relationship to the foundation of quantum mechanics looks pretty sketchy compared to a more careful analysis.

More wholly:
$$F\left(x,\cdots,x_n\right)\equiv1\equiv{m_e}{e^4\over8c\epsilon_0^2h^3R_H}-{{\pi r_pcm_e}\over2h}$$
$x_4=h=$ Planck's constant
$x_3=\epsilon_0=$ Permittivity of vacuum
$x_2=c=$ Speed of light
$x_1=e=$ elementary charge

other useful constants and relationships:

$m_pr_p={2h\over{\pi c}}=4\ell m_{\ell}\;(Haramein's\;Equation)$

A 4th order 7D polynomial, solved for roots using numerical method:

The Surfer, OM-IV