Possibly the simplest quantum physics question EVER

[Hertz]

Homework Statement

A beam of electrons strikes a barrier with two narrow but equal-width slits. A screen is located beyond the barrier, and electrons are detected as they strike the screen. The 'center' of the screen is the point equidistant from the slits. When either slit alone is open, 10 electrons arrive per second in a very small region at the center of the screen. When both slits are open, how many electrons will arrive per second in the same region at the center of the screen? (Question 11, Chapter 4)

Homework Equations

Not really sure... This is why I'm stuck. I can't think of any equations to use to approach this type of problem.

The Attempt at a Solution

My intuitive guess is 20.. For obvious reasons. I just don't see my teacher putting such an informal and simple question on our assignment. Is there a more formal way to solve for the answer to this question?

 

[mfb]

The answer is not 20.
What do you know about amplitudes and intensities behind a double slit?
Phase difference is another keyword.

 

[Hertz]

The answer is not 20.
What do you know about amplitudes and intensities behind a double slit?
Phase difference is another keyword.

I know that all wavelengths constructively interfere in the exact center because the waves from each slit travel the same distance to the center. I also know that the maximum steadily decreases to a point some distance from the center where the waves from one slit destructively interfere with the waves from another.

This seems a little bit hard to apply though.. When I think of a "beam" of electrons, I think of one electron reaching the double slit, followed by another electron reaching the double slit, etc. I can see a single electron interfering with itself and having a probability distribution like that of an interference pattern, but what do I do with this info?

It's basically telling me the amplitude of the single slit maximum right? I'm not sure how to use this to find the amplitude of the double slit maximum.

 

[mfb]

I can see a single electron interfering with itself and having a probability distribution like that of an interference pattern, but what do I do with this info?

What do you know about the phases from the two slits, what do you know about amplitudes and their relation to intensities?

It's basically telling me the amplitude of the single slit maximum right?

You have something related to the amplitude.

 

[Hertz]

What do you know about the phases from the two slits, what do you know about amplitudes and their relation to intensities?

Are you hinting at amplitude and intensity being proportional to each other? I'm sorry, I'm still very confused... What do you mean by the "phases between the two slits"? Are you talking about the difference in distance (Δx) traveled by the electron as compared to the wavelength of the electron? If I know Δx and the wavelength of the electron, the only thing I personally know how to do with this is locate the minima and maxima, I don't know how to find the intensities of these minima or maxima... Furthermore, I don't know how to relate these intensities with the given intensity of the single slit maxima..

 

[mfb]

Are you hinting at amplitude and intensity being proportional to each other?

They are not proportional to each other.

What do you mean by the "phases between the two slits"? Are you talking about the difference in distance (Δx) traveled by the electron as compared to the wavelength of the electron?

Right.

Fill in:
You know that the distance from both slits to the maximum is the same. This means ____ interference between both (=you have a ____).

Amplitudes from different sources (different slits) can be _____ to get the overall amplitude.
Let's assume the amplitude with just the first slit is 1 (units don't matter here). The amplitude with just the second slit is 1 as well due to the symmetry. If both slits are open, you can _____ the amplitudes and the result is _____ (due to the first "___").

The relation between intensity and amplitude is in your textbook, and nearly every description of the double-slit experiment. Once you have the amplitudes (for 1 and for 2 slits), the intensities are easy to calculate.