On closer inspection,
only solutions with \(v^2=0\) at \(x=x_z\) are admissible in the post "Twirl Plus SHM, Spinning Coin" date 17 Jul 2015.
\(\theta\) could be polarization measured from the vertical. Photons emission/absorption occurs at \(x=x_z\), at the center of the \(\psi\) cloud.
What if \(\theta\) can be tuned, at 45o, the factor,
\(1-\sqrt{\cfrac{sin(\theta)}{cos(\theta)}}=0\) and
\(E_p=0\)
when \(\theta=45^o\),
does the particle also vanishes? It is no longer emitting nor absorbing photons.