$\psi$ All Over The Place

Why is $\psi$ all over the place but $E=h.f$ take on discrete values?

$\psi$ is measured as energy density (Jm^-3).  It is a standing wave wrap around the center of the particle.  That is why it is all over the place.  As a wave it can superimpose and create a bigger wave.  Many $\psi$ waves of the same type sum to create particle clouds.  Earth itself is one big $g^{-}$ particle, that is the superposition of many $\psi$s from many $g^{-}$ particles.

Numerically $\psi$ equals the Newtonian force.  It is expected that under equilibrium when all forces sum to zero, that $\psi$ of a particle is equal to the $\psi$ of its neighboring particles.  As a wave, the frequency, $f$ of $\psi$, measures its energy.  This is consistent with Planck equation,

$E=h.f$

Planck equation, provides energy information of a particle as a whole.  As a complete wave around the particle, $\psi$ can only take on certain frequencies such that the wave are of integer multiple of wavelengths on the perimeter of a circle, center at the particle.

$n.\lambda_{\psi}=2\pi a_\psi$

and

$n.\lambda_{\psi}mc=2\pi a_\psi mc=h.f=E$

for $n=0,1,2,3...$

It is expected that as $E$ changes, $\psi$ around the particle changes correspondingly, given the total volume of $\psi$.  The energy of $\psi$, $E$ takes on discrete values.

$\psi$ itself is all over the place.