Polarization And Invisibility

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 45^o, 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.