Electron Diffraction - One Electron Through Double Slit

[cragar]

When we fire one electron through a double slit , can't we still get a diffraction pattern even when firing just one electron.

 

[cragar]

come on someone has to have some input on this

 

[ExtravagantDreams]

A single electon will create a single spot on a flourescence screen, hardly a diffraction pattern.

But, quantum mechanics mantains that each electron will still follow the rules of feynmann paths. Hence, it is in a superposition of all pathes and will on average create a diffraction pattern. In other words, if you shoot many many electrons through the slits one by one, the a diffraction pattern will appear the same as if you shot them all at once (ignoring coulomb interaction)

 

[cragar]

i see

 

[rcgldr]

When the electrons are shot thorugh a slit, why is it assumed that the original electrons are the ones that end up exiting the slit, and not some interchange between the original electrons and the electrons from the molecules on the edges of the slit, similar to the way that photons are captured and new photons released when refracted or reflected?

 

[cragar]

interesting

 

[PhilDSP]

However a single electron passing through a very, very thin layer of gold foil will produce a diffraction pattern. Look up G. Thomson's experiments.

 

[ExtravagantDreams]

When the electrons are shot thorugh a slit, why is it assumed that the original electrons are the ones that end up exiting the slit, and not some interchange between the original electrons and the electrons from the molecules on the edges of the slit, similar to the way that photons are captured and new photons released when refracted or reflected?

Well, there is some interaction due to the edges, which is why one can obtain diffraction from a single slit. The electrons usually have low enough energy that they elastically scatter. Actually to clarify, Young's double slit experiment refers to interference, due to the two slits. It also has diffraction due to edge effects. This results in a diffraction pattern modulated by the interference condition. i.e. Fourier transform of a convolution is the product of Fourier transforms.

However a single electron passing through a very, very thin layer of gold foil will produce a diffraction pattern. Look up G. Thomson's experiments.

No, again a single electron by itself can not produce an entire diffraction patter. When you measure this electron's position it exists only in one state. The collection of individual electrons will lead to the pattern due to statistics.

I presume you mean the Rutherford et al. experiment (based on Thomson's theoretical model). It's essentially a very basic LEED experiment.

 

[cragar]

ok when they fire the electrons one at a time through the double slit , after a while they get an interference pattern , if they shoot them one at a time how come they don’t all go the same place , why do we get a diffraction pattern if we shoot them one at a time .

 

[ExtravagantDreams]

Quantum mechanics! It's a problem of statistical mechanics really. Individual particles don't move in a deterministic fashion, but with probabilities.

The reason there is still an interference pattern is that each particle has a probability of going on some particluar path. Since the particle acts like a wave in this case, by superposition of all paths, some final destinations are more probable than others.

 

[cragar]

i see , thank-you

 

[PhilDSP]

No, again a single electron by itself can not produce an entire diffraction patter. When you measure this electron's position it exists only in one state. The collection of individual electrons will lead to the pattern due to statistics.

I presume you mean the Rutherford et al. experiment (based on Thomson's theoretical model). It's essentially a very basic LEED experiment.

That was George Paget Thomson in Scotland (J. J. Thomson's son) who was the second to verify the De Broglie hypothesis of "matter waves" associated with electrons, shortly after Davidsson and Germer. And those were indeed single electrons which elicited a diffraction pattern that could be photographed. He could vary the velocity thtt the electrons were fired and the size of the diffraction radius would change.

In some instances, as you're apparently pondering, phonons are excited in an otherwise stationary material. But for the gold foil experiment, the wave is associated directly with the solitary traveling electron. But maybe there are still folks who don't believe the de Broglie hypothesis is real?

 

[SpectraCat]

That was George Paget Thomson in Scotland (J. J. Thomson's son) who was the second to verify the De Broglie hypothesis of "matter waves" associated with electrons, shortly after Davidsson and Germer. And those were indeed single electrons which elicited a diffraction pattern that could be photographed. He could vary the velocity thtt the electrons were fired and the size of the diffraction radius would change.

In some instances, as you're apparently pondering, phonons are excited in an otherwise stationary material. But for the gold foil experiment, the wave is associated directly with the solitary traveling electron. But maybe there are still folks who don't believe the de Broglie hypothesis is real?

I think the issue here is semantic, but still important. George Thompson fired a beam of electrons through the gold foil to measure the diffraction pattern, thus demonstrating the wave-nature of massive particles. I do not know for certain that he actually fired them one at a time (space-like separation between electrons) in the original experiment, but that experiment has ceratinly subsequently been done, and with similar results (i.e. a diffraction pattern).

So, a single electron cannot be measured in more than one place on a detector screen, so it cannot possibly make a diffraction pattern ... it makes a dot. However the probability distribution of a single electron is a diffraction pattern, as can be verified by making multiple measurements. Clear?

Incidentally, it's kinda cool that J.J. Thompson won the Nobel prize in physics for showing that electrons act like particles, and then his son won it a couple of decades later for showing that electrons act like waves. Nice complementarity there!