${S\over O}=1$ ; justification: energy and mass are conserved, lossless system
${S\over O}={A\over{1+A\beta}}$
$1={R_\infty\over R_H}-{m_e\over m_p}$ & (using $m_e\over m_p$ instead of ${{\pi r_pR_H}\over \alpha^2}$)
$R_\infty={m_ee^4\over 8{\epsilon_0}^2h^3c}$
(will fill in math steps later, refer to The Universe is a Feedback System)
$A_v={S\over O}={A\over{1+A\beta}}$
$A_v=1$
$1+A\beta=A$
$1=A-A\beta$
$A={m_ee^4\over 8{\epsilon_0}^2h^3cR_H}$
$\beta={{8{\epsilon_0}^2h^3cR_H}\over{m_pe^4}}$
A, open loop forward gain:
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| This is approximately equal to 1 due to artificial tuning of constants |
$\beta$, reverse gain:
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* Universe of a Hydrogen atom
Moar later.
These values of $A$ and $\beta$ are reminders that this equation and this problem is rooted in the physical single hydrogen atom - a dynamic between a proton and electron. This mathematical tool of transforming the equation to an analogous "system", one can pull out key features (with good math tools/models). The dynamic between the proton and electron captured in a simple diagram. The hydrogen atom, 1H, has a full analytical solution (full Wave Equation or combined Schrรถdinger wave equation for both proton and electron or however it's done).
