Wave nature of electron, interference and standing waves

[fusun]

Hello,

was wondering a couple of details on the wave nature of electrons and the state of the art in this field. In particular:

• Is it practical and possible (easily) to create a cm sized electron interference pattern (fringes are in the cm size magnitude). I have so far seen Low Energy Electron Diffraction (LEED) which seems to be able to create wave lengths that are permissive to this kind of thing...
  
• Is it possible to create a standing wave of electrons similar to the way a microwave oven creates standing microwaves (with hot and cool spots).
  
• What does it mean from a quantum perspective for an electron to be constructively/destructively interfered with? Does its charge get "amplified" the same way a light wave becomes brighter?
  

I'm asking all this because I'm wondering if there's a way to exploit the wave nature of electrons to create very deep electrostatic potential wells.

Appreciate the info.

 

[ibysaiyan]

I am not much knowledgeable in this area but having read your post, I assume you think electrons to act as waves and not as wave-function.. to answer your point no. 2 ; I suppose by standing waves you mean 'stationary ones' ,so in this case there will be needed two opposite waves to super-pose on each other.. hm...
I think from quantum perspective it doesn't matter what size the particle is as long as Quantum effects are noticeable.
So everything applies same to each particle in the case of fringes.. isn't that a set of outcomes for the respective wave-function ?

P.S: It's almost 3 am ,sorry if I am rambled along..

 

[Drakkith]

• Is it practical and possible (easily) to create a cm sized electron interference pattern (fringes are in the cm size magnitude). I have so far seen Low Energy Electron Diffraction (LEED) which seems to be able to create wave lengths that are permissive to this kind of thing...

• 
  
  It really depends on what you mean by practical. For electrons you need the electron source, a container, target, and all that inside a vacuum container. Throw in the vacuum equipment and it's not looking very cheap from an individuals viewpoint.
  
  

  [*] Is it possible to create a standing wave of electrons similar to the way a microwave oven creates standing microwaves (with hot and cool spots).

  
  Not sure.
  
  

  [*] What does it mean from a quantum perspective for an electron to be constructively/destructively interfered with? Does its charge get "amplified" the same way a light wave becomes brighter?

  
  No, the interference only refers to the probabilities of an electron being found in a particular location. A black area on the pattern is just a spot where an electron has a very low chance of being found. The pattern you usually see is the result of many many electrons being detected over time. An electron doesn't spread it's charge out all over the place.
  
  

  I'm asking all this because I'm wondering if there's a way to exploit the wave nature of electrons to create very deep electrostatic potential wells.

  
  I'm sure you can use the wave nature to do different things to an already established well of electrons, but to create that well you need to force them together against their repulsive forces.

 

[ibysaiyan]

It really depends on what you mean by practical. For electrons you need the electron source, a container, target, and all that inside a vacuum container. Throw in the vacuum equipment and it's not looking very cheap from an individuals viewpoint.



Not sure.



No, the interference only refers to the probabilities of an electron being found in a particular location. A black area on the pattern is just a spot where an electron has a very low chance of being found. The pattern you usually see is the result of many many electrons being detected over time. An electron doesn't spread it's charge out all over the place.



I'm sure you can use the wave nature to do different things to an already established well of electrons, but to create that well you need to force them together against their repulsive forces.

I agree with your post however whilst I was reading few articles based on "double slit experiment" I recall that few mentioned the following scenario: An interference pattern is observed on the target screen when one photon is shone/ejected in the path of two slits. So am I right to think that interference pattern is observable in such case ^ .

-ibysaiyan

 

[Drakkith]

I agree with your post however whilst I was reading few articles based on "double slit experiment" I recall that few mentioned the following scenario: An interference pattern is observed on the target screen when one photon is shone/ejected in the path of two slits. So am I right to think that interference pattern is observable in such case ^ .

-ibysaiyan

I can't see that being possible. One photon is only detectable in ONE spot. I really don't think it is possible to make a pattern from one photon. Do you have a link to the references you were reading?

 

[fusun]

It really depends on what you mean by practical. For electrons you need the electron source, a container, target, and all that inside a vacuum container. Throw in the vacuum equipment and it's not looking very cheap from an individuals viewpoint.

Practical like getting a bunch of discarded cathode ray tubes from old CRTs etc.

No, the interference only refers to the probabilities of an electron being found in a particular location. A black area on the pattern is just a spot where an electron has a very low chance of being found. The pattern you usually see is the result of many many electrons being detected over time. An electron doesn't spread it's charge out all over the place.

I can't see that being possible. One photon is only detectable in ONE spot. I really don't think it is possible to make a pattern from one photon. Do you have a link to the references you were reading?

Yes of course. The result of the fringes is that the probability of an electron landing somewhere in particular is heightened, but the electron is still an electron.

This would mean that the ion beam density (macro effect) could be amplified creating a highly charged hot spot where most electrons hit.

Now that I think about it, this is obvious.

[*] Is it possible to create a standing wave of electrons similar to the way a microwave oven creates standing microwaves (with hot and cool spots).

Not sure.

http://en.wikipedia.org/wiki/Low-energy_electron_diffraction" of an electron at room temperature seems to be 8nm. (No source).

The De Broglie relation gives the wavelength of an electron at 20eV to be:

lambda = h / p = 4.13*10^-15 / (20x1.6x10-19 / 2.99 * 10^8) = 4.13*10^-15 / (10.70 * 10^-11) = 6.1 * 10^-4m = 6mm.


Does anyone else follow the steps I took? would this be reasonable?

 

[fusun]

I assume you think electrons to act as waves and not as wave-function..

Good point. I had confounded the two different phenomena into one when posting. Indeed, there is the phenomena of getting diffraction (which is purely a probability distribution function) and standing waves (which is a De Broglie wave form phenomena).