Zee Squared

In the post "One Plus One Plus One" dated 18 Dec 2014,

$\psi$, $F$ and $q$ all adds up.  At the plateau, for $Z$ number of particles,

$ln(cosh(\cfrac { G }{ \sqrt { 2{ mc^{ 2 } } }  } x_z))\rightarrow Z*ln(cosh(\cfrac { G }{ \sqrt { 2{ mc^{ 2 } } }  } x_z))=Z$

So,

$\psi_n\rightarrow Z*\psi_n$

and under the strict condition,

$\cfrac { \psi _{ d } }{ m } =2{ c^{ 2 } }cos(\theta )ln(cosh(\cfrac { G }{ \sqrt { 2{ mc^{ 2 } } }  } x_z))$

from the post "Twirl Plus SHM, Spinning Coin" dated 17 Jul 2015, $\psi_d$ is the displacement of $\psi$ in the containing $\psi$ cloud that performs $SHM$.  So,

$\cfrac { \psi _{ d } }{ m }\rightarrow Z*\cfrac { \psi _{ d } }{ m }$

but $\psi_{max}$ is still one particle, $n=77$ (as defined),

$\psi_{max}=1$

with $m\,\,or\,\,m_{\rho}=\cfrac{1}{2c^2}*\cfrac{1}{2.4438}$

so,

$v^{ 2 }_{ { max } }=-Z*\cfrac { \psi _{ d }}{ m } Z*\cfrac { \psi _{ n } }{ \psi _{ max } }\  e^{ \psi _{ max } }\left( { e^{ 2\psi _{ max } }-1 } \right) ^{ 1/2 }$

thus,

$v^{ 2 }_{ { max } }\rightarrow Z^2*v^{ 2 }_{ { max } }$

Note:  I have a few missing posts on the new mode of oscillations; of SHM within $\psi$.

$\psi_{d}=\psi_{max}-\psi_n$ --- (*)

is only for a particle of $\psi_{max}$ receiving a particle of $\psi_n$, as the scenario is developed in the post "Twirl Plus SHM, Spinning Coin" dated 17 Jul 2015.  $\psi_d$ is the displaced $\psi$ in $SHM$ in general and is not restricted to (*).

Note: If $\psi_{max}$ is also scaled then all the particles in the expression for $v_{max}$ is scaled by $Z$ which lead back to the situation without scaling.