\(v^2_{min}=tanh(2(x-x_z))\cfrac { sinh^{ 2 }(x-x_z) }{ 2ln^{ 2 }(cosh(x-x_z)) }\)
with a Gaussian distribution of mean, \(\mu=1\) and spread \(\sigma=0.25\)
\(v^2_{min}\),
and the result of convolution,
when inverted,
where the valid region is over the extend of \(v^2_{min}\) between lines \(a\) and \(b\).
This is the distribution of energy, \(KE\) of a population of particle confined in another particle excited by a non zero \(\psi_c\).
Another flat top.
