Big Particle, A Lot Of Noise

From the post "Another Take On Discrete",

$x=e^{ -\cfrac {A( x-1) }{ n^{ 2 } }  }$

where $x=1$ is an immediate solution.  It is a unit circle onto which $n$ cycles of wavelength $\lambda$ can be packed, where $n\in Z^{+}$, $0\lt n\lt n_{\infty}$, and $n_{\infty}\rightarrow\infty$.

$2\pi.x=2\pi=n\lambda$

Although not a "natural" solution for a particle of unit radius (1 m in SI units), it is a valid solution to the equation for $\psi$.  If a particle can be sufficiently isolated (1 m radius), then it can be a high frequencies, ultra-broadband, discrete frequency resonator.

And be made to resonate at,

$f=\cfrac{nc}{2\pi}$

for $n=1,2,3...$

Very interesting.