User:Tohline/Appendix/CGH/QuantumTransitions

Speculation Regarding Quantum Transitions

The contents of this "Ramblings Appendix" chapter are pure speculation. I am definitely not an authority on quantum mechanics, but I have for some time been interested in interpretations of the wave function. It is this, along with my quantitative interests in digital holography, that have led to the set of thoughts presented below.

Digital Holography

When a ray of coherent, monochromatic light passes through a square aperture, a specific diffraction pattern is created. The same result is achieved by bouncing the light off of one side of a cube [serving as the square aperture]. In this manner, information about a localized structure (the aperture) is preserved in a (diffraction) pattern that formally extends to infinity. A hologram is created by "storing" the diffraction pattern (amplitude with no phase) as an image.

This process can be reversed. A ray of coherent, monochromatic light that bounces off of (or shines through) the holographic image will — at the appropriate distance from the hologram — display an image of the original compact aperture.

Note that, either way — that is, whether the aperture is being used to create the diffraction pattern or vise versa — the diffraction pattern/hologram can be viewed as a probability distribution.

Quantum Wavefunction

This sounds suspiciously like photoemission or an atomic transition:

1. Let's say that when an electron is bound to a nucleus in a particular energy state, this state is represented by a "surface" — perhaps it should be a more volume-filling structure — whose multiple-aperture/grid structure (each subgrid square aperture having a different, specified opacity) both appropriately represents the wavefunction and defines a hologram. In this manner, when an electron is bound to an atomic nucleus, information regarding its position/momentum is viewed as a wave function (probability distribution).
2. PHOTOIONIZATION:   When a photon (of the proper frequency) strikes the atom, it can react with the wavefunction in such a manner that it ejects the electron. That is to say, the result of the light passing through (bouncing off of) the wavefunction (hologram) is to form a compact entity (the electron) that is moving away from the atomic nucleus.
1. Note that if the incident ray of light has an incorrect frequency and/or hits the hologram at an incorrect angle, the resulting diffraction pattern does not generate the compact entity (electron). But it is natural to expect that the likelihood that the photon hits with the correct angle of incidence will be higher for axisymmetric wavefunctions (holographic surface) and will be even higher in the case of spherical symmetry.
2. The direction the electron gets ejected should naturally be at a well-defined angle with respect to the direction of incidence of the initial ray of light (photon).
3. EXCITATION (BOUND-BOUND TRANSITION):   Perhaps the holographic surface is flexible, permitting it to undergo oscillations. The eigenfunctions corresponding to various modes of oscillation might in some way be associated with the holograms that represent other acceptable bound orbital levels. Then if the frequency of an incident photon resonates with one mode's associated oscillation eigenfrequency, the holographic structure could change to indicate that the electron has moved to a different orbital level.

See Also

• Tohline, J. E., (2008) Computing in Science & Engineering, vol. 10, no. 4, pp. 84-85 — Where is My Digital Holographic Display? [ PDF ]
• Diffraction (Wikipedia)
• Various Google hits:
  • Single Slit Diffraction (University of Tennessee, Knoxville)
  • Diffraction from a Single Slit; Young's Experiment with Finite Slits (University of New South Wales, Sydney, Australia)
  • Single Slit Diffraction Pattern of Light (University of British Columbia, Canada)
  • Fraunhofer Single Slit (Georgia State University)
• Hydrogen Atom (Wikipedia)

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