It seems Compton scattering experiment can be used to determine location of electron by hitting it with photon. But nowhere on wiki article (https://en.wikipedia.org/wiki/Compton_scattering) for Compton scattering It mentions the Heisenberg uncertainty principle. Can someone please explain how uncertainty principle applies to Compton scattering.
As per Compton scattering. if we measure λ' , λ and θ accurately; the location of electron can be determined.(in theory).
λ' - λ = h(1-cosθ)/m*c
Also.
Δx = c * Δ t and Δp = hc/λ -hc/λ'
Sumit Garg
The English wikipedia article only talks about Doppler shift; in this regard whoever wrote on this topic for the German edition did a better job also addressing Doppler broadening. Doppler broadening, if it occurs, tends to "overpower" natural (i.e. uncertainty caused) widths of phenomena. That's why in many spectroscopies we fit data with a Gaussian function (Doppler broadening) and the approximation is good enough while it would actually be a Voigt function which is a convolution of a Gaussian and a Lorentzian; the Lorentzian is the broadening contribution of the natural width.
Concluding, I also have never seen the math on the uncertainty principle for the Compton effect, so I can't guarantee it's also Lorentzian, but the reason why it's ignored is probably because there is another dominating broadening effect.
There’s a mixup: The wavelength shift refers to the photon, not the electron, as does the momentum shift. If the photon’s momentum is known precisely, its position is not, which isn’t surprising, since this describes a monochromatic wave: A delta function in momentum space is a constant function in position space and vice versa, an immediate illustration of the uncertainty principle. So to describe what happens, when scattering does occur, what’s needed is to look at the evolution of a wavepacket, whose wavelength isn’t precisely known, but whose center of mass is correspondingly known and compute the scattered wavepacket.
In more direct terms: In Compton scattering you're trying to locate an electron by ``throwing'' a photon at it. There's an uncertainty principle at work regarding momentum and position of the photon-you can only ``throw'' a wavepacket, since a monochromatic wave can't describe a well-defined position of anything and those uncertainties induce corresponding uncertainties in the momentum and position of the scattered electron-which, also, depend on the uncertainties of the initial electron, since its position and momentum, similarly, are subject to the uncertainty principle. The rest is just a mathematical formalization of these statements.
- Badges
- Science topic