Can such a half wavelength standing wave exist?
All other waves have a average amplitude of zero. This half wave has a positive DC value.
Does this wave corresponds to an excited state of the particle? How exciting?!
Which would suggest that an excited state is when the wavelength of \(\psi\) collapses into longer wavelengths and thus oscillates at higher frequencies ie \(n\rightarrow 1\). The following diagram shows wave of \(n=1,2,3\) at the same distance from the center.
Where lower values of \(n\) (also the number of crests) corresponds to higher values of excitation. And the half wavelength wave \(n=0.5\),
would be the limit beyond which \(\psi\) will be at twice the present distance from the center oscillating at the level \(n=1\), a wave shaped as a circle.
\(\psi\) is not a particle, but the discontinuity of \(\cfrac{\partial\,\psi}{\partial\,x^{'}}\) around the perimeter \(2\pi x\) suggests that \(n=0.5\) may not exist.
However, where \(\psi\) oscillates between a space dimension and an orthogonal time dimension for which we have no access, then \(\psi\) can appear as a half wave in the space dimension. This \(\psi\) oscillating with half wavelength, twice the normal frequency of particles oscillating between two space dimensions, is from a photon.
The \(\psi\) of a photon oscillates between a space dimension and a time dimension. A half wave cannot exist when \(\psi\) oscillates between two space dimensions because that would introduce a discontinuity in the change of \(\psi\) along the perimeter around the particle, but a half wave can exist where \(\psi\) oscillates between one space and one time dimension. \(\psi\) simply disappears from our space reality for half the cycle.
"\(\psi\) return to the same spot after some time in the orthogonal time dimension"
Note: If \(\psi\) do not return to the same spot then the crest of this wave will be seen rotating around the perimeter, and we have an additional frequency component of \(\psi\).
This means, the first point in the data set, is the key into the orthogonal time world.
| n | \(\lambda\) (nm) | \(\cfrac { n\lambda }{ 2\pi }\) | \(n^{ 2 }ln(\cfrac { 2\pi }{ n\lambda \times10^{-9} } )\) | \(\cfrac { \lambda }{ 2\pi }\) |
|---|---|---|---|---|
| 2 | 121.567 | 38.697 | 68.270 | 19.349 |
\(\psi\) spent some time \(\Delta t\) in the orthogonal time axis. Because of \(\Delta t\), the frequency of \(\psi\) is lower than expected when \(n=0.5\), theoretically; and this shows up as a higher value for \(\lambda\) when compared with \(\lambda\) of \(n=0.5\).
