\(x_z\) is independent of \(a_\psi\). Increasing the frequency of oscillations of \(\psi\) changes \(a_\psi\) but does not change \(x_z\). Adding \(\psi\)/charges, changes the peak value of \(\psi\) at \(x_z\), but does not change \(x_z\).
It is likely that,
\(x_z=a_\psi\)
only for \(n=1\). This is without proof.
What is \(x_z\) physically? If \(\psi\) can be detected, it is the radius of the sphere confining \(\psi\). The first level of oscillations \(n=1\) is when \(a_\psi=x_z\). \(x_z\), the radius of \(\psi\) determines this fundamental frequency.
\(x_z\) is constrained by the resistance of space and time dimensions to \(\psi\). When \(\psi\) is fully manifested, the particle is has no mass. This occurs when \(\psi\) oscillates between one space and one time dimension. When \(\psi\) oscillates between two space dimensions, part of the particle is mass and part of it is \(\psi\).
Changing the resistance to \(\psi\) changes \(x_z\).
When
\(x_z=a_\psi\), \(n=1\)
changing temperature will change the resistance to \(\psi\) and so changes \(x_z\) and thus changes \(a_\psi\).
The presence of another \(\psi\) field changes \(x_z\). \(\psi\) due to the particle, gets squeezed. If the applied \(\psi\) field is oscillating then the change in \(x_z\) also oscillates and thus when
\(x_z=a_\psi\), \(n=1\)
the fundamental frequency oscillates as \(a_\psi\) oscillates.
So, the application of an oscillating magnetic/electric field will oscillates the fundamental frequency of the particle.
Note: \(\psi\) is energy density, adding densities does not change the total volume; the resulting sum is still energy per unit volume.
