I was thinking about the photon double-slit experiment recently, where a single photon is passed through two narrowly-spaced slits so that it delocalizes (passes through both slits), undergoes constructive and destructive interference with its own wavefunction, and eventually forms a telltale pattern of bright and dark stripes on the screen. I know, however, that there is always a chance that the photon could be absorbed or scattered along the way to the detection screen - so my question is, what equations could be used to describe this probability of such an interaction? All the equations I know for photon absorption (i.e. Einstein's A and B coefficients) treat the photon as an oscillating electric field passing by a molecule, so I am curious how the transition probabilities would change if the photon is delocalized and only half of its wavefunction is passing through a certain region (i.e. the bit of air just beyond one of the two slits).
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It's a matter of discussion whether the photon passes both thru both slits or one ... many would say we do not know which slit the photon traverses. But we do know the trajectory is effected by both slits as the "pattern" results. The Feynman path integral is a good method to calculate the pattern. – PhysicsDave Jan 21 '23 at 05:22
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Also the excited electron is already giving off virtual photons ... which likely travel thru both slits .... eventually energy is transferred in terms of the "real" photon. – PhysicsDave Jan 21 '23 at 05:25
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Double slit question - wavefunction collapse – HolgerFiedler Jan 22 '23 at 07:03
1 Answers
The photon is an elementary particle in the mainstream model. All elementary particles remain intact as far as the theory goes, which models their probabilistic behavior with quantum field theory (QFT), unless there is an interaction or decay for which the mathematical model has predictions of the probability distributions.
I will try to clarify your miss-conceptions.
the photon double-slit experiment recently, where a single photon is passed through two narrowly-spaced slits so that it delocalizes (passes through both slits),
It is not the photon that delocalizes in the QFT used to model the double slit experiment. The photon passes through one or the other slit , what delocalizes is the wave function, the probability of going through one or the other slit.
undergoes constructive and destructive interference with its own wavefunction,
It is the wave function that undergoes interference, the wave function that models the scattering of a photon on two slits of definite width and distance apart.
and eventually forms a telltale pattern of bright and dark stripes on the screen.
That pattern is the probability distribution, $Ψ^*Ψ$, where $Ψ$, is the wavefunction for the scatter.
I know, however, that there is always a chance that the photon could be absorbed or scattered along the way to the detection screen - so my question is, what equations could be used to describe this probability of such an interaction?
If this happens, it means the photon has interacted/scattered on the molecules and a new wavefunction should describe it from the scatter onward.
All the equations I know for photon absorption (i.e. Einstein's A and B coefficients) treat the photon as an oscillating electric field passing by a molecule,
Those treat with classical electrodynamics electromagnetic radiation, light. Not single photons and wavefunctions.
so I am curious how the transition probabilities would change ,
They would change, but the smart physicist would use the classical electrodynamics on the end results , with its absorptions etc coefficients, because it would be too complicated mathematically to do that with photon scatters. There is continuity built in on purpose since solutions of Maxwell equations model both, the mathematical form of quantum mechanics,QED, and the classical electrodynamics.
if the photon is delocalized and only half of its wavefunction is passing through a certain region (i.e. the bit of air just beyond one of the two slits).
It is confusing the two frames, classical and quantum, to be thinking of half a wave function. As I say above, if there is a scatter a new wavefunction is needed to model the probability distributions.
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