B Some very basic questions around the double slit experiment

[rede96]

I have a few basic questions about the double slit experiment and was hoping someone might be able to answer them.

1) How far apart from each other would have I have to make the slits so effectively no detection took place? E.g. is there a limit to how far the wave function can spread and a detection still take place?

2) I am assuming that the orientation of the slits is irrelevant? E.g. I'd still see the same interference pattern if the slits were horizontal or even at some angle?

3) If I removed the screen with two slits and just fired electrons one at a time at a target area, what sort of distribution would I see? E.g. would I I see a circular distribution around the target point? Would there be less electron being detected further away from the target point?

4) Has the experiment ever been done with two sets of slits? Say with the second set of slits at some distance away from the first and at a different distance apart? I was just trying to understand if there has to be a direct line of sight between the source and the detection point for a detection to take place or if the wave like property would still lead to a detection even if there was no direct line of sight?

Thanks

 

[DennisN]

2) I am assuming that the orientation of the slits is irrelevant? E.g. I'd still see the same interference pattern if the slits were horizontal or even at some angle?

The interference pattern, that is, the "line of dots", will always be perpendicular to the orientation of the slits. So if you rotate the slits, the pattern will also be rotated.

 

[BvU]

4) Has the experiment ever been done with two sets of slits? Say with the second set of slits at some distance away from the first and at a different distance apart? I was just trying to understand if there has to be a direct line of sight between the source and the detection point for a detection to take place or if the wave like property would still lead to a detection even if there was no direct line of sight?

You could do such a thing but wouldn't learn anything new. Note that even with one single slit, you already don't have the direct line of sight from the source, only from the slit. See the nice animations here

 

[BvU]

1) How far apart from each other would have I have to make the slits so effectively no detection took place? E.g. is there a limit to how far the wave function can spread and a detection still take place?

If you have a flat wave front (as in those animations), the double slit pattern can be pretty far apart. Of course the interference peaks would crawl ever closer together. There is no theoretical limit but intensities go down rapidly for large angles of diffraction.

 

[BvU]

3) If I removed the screen with two slits and just fired electrons one at a time at a target area, what sort of distribution would I see? E.g. would I I see a circular distribution around the target point? Would there be less electron being detected further away from the target point?

Depends on how you generate the beam. Google 'electron beam collimaton' or 'beam collimaton'

 

[Nugatory]

I have a few basic questions about the double slit experiment

You could save yourself just a ton of grief by learning how to solve the double slit for ordinary classical electromagnetic waves. There's a reason why that problem appears in the undergraduate physics curriculum before introductory QM.

 

[rede96]

The interference pattern, that is, the "line of dots", will always be perpendicular to the orientation of the slits. So if you rotate the slits, the pattern will also be rotated.

I thought was the case but just wanted to check. Thanks for the reply.

 

[rede96]

You could do such a thing but wouldn't learn anything new. Note that even with one single slit, you already don't have the direct line of sight from the source, only from the slit. See the nice animations here

If you have a flat wave front (as in those animations), the double slit pattern can be pretty far apart. Of course the interference peaks would crawl ever closer together. There is no theoretical limit but intensities go down rapidly for large angles of diffraction.

Depends on how you generate the beam. Google 'electron beam collimaton' or 'beam collimaton'

That's great info, thanks for that. I'll have to read and digest as I'm just an interested layman and not great with math side of things. But that's what I was looking to understand more.

 

[rede96]

You could save yourself just a ton of grief by learning how to solve the double slit for ordinary classical electromagnetic waves. There's a reason why that problem appears in the undergraduate physics curriculum before introductory QM.

Thanks for the reply. Unfortunately at 52 years old and just basic high school math I can usually only aim to understand things conceptually. I really wish I had more time to learn all this properly!

But I'll definitely have a look for some video lectures on classical em waves.

 

[BvU]

Thanks for the reply. Unfortunately at 52 years old and just basic high school math I can usually only aim to understand things conceptually.

Kudos !

Conceptually the things to pick up are:

narrow slits give wide diffraction patterns
peaks are closer if wavelengths are smaller​

and, more broadly:

with smaller wavelengths you can 'see' (observe) smaller things -- the reason an electron microscope can explore where a light microscope can not; and the reason these particle physicists need ever bigger machines to study ever smaller structures​

The underlying math is Fourier analysis -- decomposing a function into sine waves. A very, very important tool in many branches of science and technology; wonderful videos aplenty on the net. Worth investigating !

 

[rede96]

Kudos !

Conceptually the things to pick up are:

narrow slits give wide diffraction patterns
peaks are closer if wavelengths are smaller​

and, more broadly:

with smaller wavelengths you can 'see' (observe) smaller things -- the reason an electron microscope can explore where a light microscope can not; and the reason these particle physicists need ever bigger machines to study ever smaller structures​

The underlying math is Fourier analysis -- decomposing a function into sine waves. A very, very important tool in many branches of science and technology; wonderful videos aplenty on the net. Worth investigating !

Thanks for the link, I'll have a good search around.

Depends on how you generate the beam. Google 'electron beam collimaton' or 'beam collimaton'

All I was trying to understand here is if I simply fire electrons one at a time from a source to a screen that detects them, what pattern would I see?

I would image I would see the particle nature of the electron hitting the screen and causing a 'dot' but it would be the wave function that would decide where the electron hit the screen. So although there is some randomness as to where the electron will hit the screen, if I allowed the pattern to build up I'd start to see circles forming on the screen that detects the electrons. The inner circles would have more 'dots' and the outer circles fewer.

Does that make sense in very broad terms?

 

[BvU]

if I simply fire electrons one at a time from a source to a screen that detects them

Whhat source do you have in mind (see #5) ?

A screen that lights up when an electron hits it is a good detector. There is no reason for circles to become visible; you would just see a blob if you took a long exposure time picture -- but perhaps I interpret your terminology wrongly ?

Things become different when you use a small circular hole in the beam path. The you do get a 2D 'equivalent' of the single slit pattern again as shown here

 

[rede96]

Whhat source do you have in mind (see #5) ?

If you'll excuse my ignorance, what difference does the source make? An electron is an electron. I didn't think it would behave differently depending on the source? But I haven't had time to look up the different sources yet, but was thinking of one that just fired a single electron at a time.

A screen that lights up when an electron hits it is a good detector. There is no reason for circles to become visible; you would just see a blob if you took a long exposure time picture -- but perhaps I interpret your terminology wrongly ?

Sorry, I can be pretty crap at explaining myself so thanks for being patient with me. What I was trying to visualize was the pattern that would be generated over time by electrons being fired one at a time at the screen. Obviously each electron will not hit the screen in exactly the same position. I would imagine there would be some variance just because the electron generated may leave the source at a slightly different angle wrt to the screen each time it is generated.

But ignoring that process variation for a moment, even if the electrons trajectory was exactly the same each time, I thought that where the electrons hit the screen would be probabilistic due to the wave function. But if I observed enough electrons, over time I'd see a pattern (assuming I could measure to enough resolution) and I thought that pattern would be circular with more electrons detected near the center of the patter and less so further away.

Does that make sense?

 

[Mentz114]

If you'll excuse my ignorance, what difference does the source make? An electron is an electron. I didn't think it would behave differently depending on the source? But I haven't had time to look up the different sources yet, but was thinking of one that just fired a single electron at a time.
Sorry, I can be pretty crap at explaining myself so thanks for being patient with me. What I was trying to visualize was the pattern that would be generated over time by electrons being fired one at a time at the screen. Obviously each electron will not hit the screen in exactly the same position. I would imagine there would be some variance just because the electron generated may leave the source at a slightly different angle wrt to the screen each time it is generated.

But ignoring that process variation for a moment, even if the electrons trajectory was exactly the same each time, I thought that where the electrons hit the screen would be probabilistic due to the wave function. But if I observed enough electrons, over time I'd see a pattern (assuming I could measure to enough resolution) and I thought that pattern would be circular with more electrons detected near the center of the patter and less so further away.

Does that make sense?

If the electrons are represented by wave packets you'll get a bivariate Gaussian with zero correlation. Which looks like what you expect.

https://en.wikipedia.org/wiki/Multivariate_normal_distribution

 

[BvU]

Makes perfect sense. But making a beam of electrons is a complicated business in itself. You can have a cloud of electrons around e.g. a cathode but then you still need to give them a momentum along the beam axis (cathode ray tube -- ignore the deflection plates) while limiting the variance in transverse momentum (by using a small aperture in the positive anode, at the cost of lower beam intensity). You can imagine that the size of the aperture determines the size of the blob on the screen. With very, very small aperture sizes we are back to diffraction patterns again -- but those sizes are really very small: an aperture of one nanometer is of the order of six wavelengths of e.g. a 50 eV electron .