# Single electron single slit interference

1. Nov 14, 2012

### cubozoan

single electron diffraction through single slit

Hi Guys

Wondered if you could help me.

Say a high energy electron (low wavelength?) is fired through an arrangement of atoms (single slit). How does a single electron hit a detector / screen according to a diffraction pattern? I understand that one electron will just flash on the screen but if you took notice of positions from other single electrons you would see the probability distribution.

I understand a beam of electrons will produce a diffraction pattern due to their wavefunction interfering constructively and destructively. But what about single electron?

How does it 'interfere' with itself?

I would like a simple explanation as it is for a-level (16 - 17 year old student).

I guess there is just something simple i am missing. Hope I have given enough information.

Kindest regards

Andy

2. Nov 15, 2012

### Simon Bridge

It is the same for a single electron - the key is to realise that the wave-function is statistical... it is the same statistical distribution for one electron or many.

If you fired a machine-gun at a target, you'd get a distribution of holes.
From that you can work out the probability that any single bullet will arrive at a particular position on the target. Fire just one bullet and you get one hole. Do lots of single bullet experiments and you can see the distribution emerge. You have no problem with the idea that bullets can have continuous probability distributions and yet remain particles?

Same with the electrons - you fire just one electron you get one flash in the detector at some position. If you repeat the experiment lots of times, you notice that the distribution of flashes (from a lot of single-electron experiments remember) follows the interference pattern.

The idea that the electron somehow interferes with itself is also misleading - wavefunctions, being statistics, are not physical and cannot interact with itself in the way that, say, ripples in a water tank do.

You'll need some patience here - it will take a while for your courses to be able to fill you in with more than half-baked descriptions.

For further information:
http://vega.org.uk/video/subseries/8
... this series of 4 lectures from Richard Feynman should advance your understanding.

3. Nov 15, 2012

### robinpike

But I thought the suggestion of interference came about because, when the diffraction pattern from a single slit is compared to the diffraction pattern from two slits, it is found that the probability of where the electron goes after passing through the single slit, is in some places, reduced by having the second slit open.

So the question is why, by opening the second slit, does it effect where the electron goes when it goes through the first slit?

4. Nov 15, 2012

### Staff: Mentor

You get the same pattern eventually, if you fire one electron at a time through the apparatus, no matter how slowly. If you send a million electrons through the apparatus, you end up with the same distribution on the screen (except for small random variations that are in agreement with the laws of statistics) regardless of whether you send them all through in one millisecond, or in a million hours.

We don't know the answer to this question, in the sense that I suspect that you're looking for. Standard quantum mechanics simply does not address questions like what is "really really" happening to a single particle, that explains why it ends up at a particular location. There are various interpretations of QM that attempt to provide answers to such questions, but so far there is no way to distinguish between them experimentally. All we can ever predict is probabilities, not the precise outcome for any single particle.

5. Nov 15, 2012

### Staff: Mentor

Re: single electron diffraction through single slit

You need low-energy electrons to see diffraction (see Wikipedia, for example) - otherwise the wavelength is so short that the path is nearly classical.

Even there, each electron interfers with itself.
Unless you develop an electron laser (this is not the same as a free-electron-laser! That emits photons) which emits coherent electrons.

Quantum mechanics ;)

6. Nov 15, 2012

### sophiecentaur

The way the electron behaves is according to the statistics that a wave treatment predicts. If you accept that, then you can move on and see what wave theory tells you. You can then discuss light, radio, sound, water waves with the same maths. I first approached all this when dealing with radio antennae, when I learned that you can 'multiply' the patterns of a basic element by the pattern of an array of elements.

When people calculate the two slits pattern, they often neglect the fact that each slit has its own pattern because that pattern is so wide in comparison with that of the two wider separated slits. The pattern for two 'infinitely thin' slits is shown here.
A single narrow slit must have finite width in order for any energy to get through) will have a very broad, single peak with small side peaks. The intensity pattern is actually a sin(x)/x shape (see this link).

If you then want to find the pattern of two real slits, you can treat the slits as an array of two point sources (with omnidirectional patterns) and then multiply that pattern by the single (finite width) slit. This gives a better picture of what you will get. See this link

All of the above is the (correct) result, obtained by treating the problem as waves. Whether it's two synchronous radio transmitters, two slits with laser light shining through them or two slits with a beam of electrons hitting them, it's all the same. Imho, it is better to learn or accept the wave thing and then get the brain ache which you can guarantee for yourself if you want a proper answer to "which hole does the electron go through" question. There is not a satisfactory answer in terms of little billiard balls - period. QM is the only way through.

Last edited: Nov 15, 2012
7. Feb 4, 2013