Quadratic Equation Solution for $R_H$ - Rydberg Constant

Another thing to note is the Full Rydberg equation can be written as a second order polynomial for the $R_H$ (Rydberg constant) term and then THEREFORE, significantly, one COULD solve for the Rydberg constant using the QUADRATIC equation, treating all other terms as "Known constants" to see if any insight can be gained.  These notes are to keep track of idea for solutions and future blog posts.

Multiply both sides by $R_H$ to clearly see the 2nd order polynomial in $R_H$

$$R_H={{m_ee^4}\over{8\epsilon_0^2h^3c}} - {\pi r_pR_H^2\over{\alpha^2}}$$

$${\pi r_p\over{\alpha^2}}R_H^2+R_H-{{m_ee^4}\over{8\epsilon_0^2h^3c}} = 0$$

This can be used to bridge / map previous $R_H$ to a new $R_H$ that includes the electron to proton mass ratio term that was dropped during the Solid State derivation of the Quantum Theory to show what the correction terms are to the original $R_H$.

Moar later.

WolframAlpha Link for Quadratics/Roots (needs moar werk)

The Surfer, OM-IV

https://rumble.com/v1ji17f-general-flynn-responds-to-ap-hit-piece.html

Ω