Math of Electron Double Slit Experiment

In summary, the discussion revolves around finding a derivation for the "wave" patterns observed in an experiment and whether wave-particle duality is a proven theory. Some suggested approaches include using classical electrodynamics/optics and the Helmholtz equation, or the path integral method. A useful resource for this topic is a paper by Feynman and Hibbs, with a link provided by DrChinese.
  • #1
Ghost Quartz
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I'm looking for a good derivation of the "wave" patterns in this experiment. I suppose that if wave-particle duality is an obsolete idea, there must be a derivation from quantum mechanics that gets close results.
Thanks in advance
 
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  • #2
There was a thread recently called "Is wave-matter duality a proven theory" which involved a discussion about this, with some links.

That might be interesting.
 
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  • #3
How familiar are you with the description of diffraction in classical electrodynamics/optics? In nonrelativistic QT it's almost the same theory, based on the Helmholtz equation and the corresponding Green's function given the boundary conditions due to the slits.

An alternative also pretty intuitive way is the use of the path integral. This is nicely worked out in the book by Feynman and Hibbs.
 
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  • #5
the link posted by DrChinese is what I was looking for. Thank you, everyone!
 
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1. What is the electron double slit experiment?

The electron double slit experiment is a fundamental experiment in quantum mechanics that demonstrates the wave-particle duality of electrons. It involves firing a beam of electrons through two parallel slits and observing the resulting interference pattern on a screen.

2. How does the experiment relate to math?

The experiment can be described mathematically using the principles of wave mechanics, specifically the Schrödinger equation. This equation describes the behavior of quantum particles, including electrons, as waves rather than particles.

3. What is the role of probability in this experiment?

The electron double slit experiment involves the concept of probability in determining the likelihood of where an electron will land on the screen. This is because the behavior of electrons is described by a probability wave, and the interference pattern observed on the screen is a result of the overlapping of these probability waves.

4. How does the distance between the slits and the screen affect the interference pattern?

The distance between the slits and the screen affects the interference pattern by changing the spacing of the fringes. When the distance is increased, the fringes become closer together, resulting in a wider interference pattern. When the distance is decreased, the fringes become further apart, resulting in a narrower interference pattern.

5. Can this experiment be used to demonstrate the principles of quantum mechanics?

Yes, the electron double slit experiment is often used as a demonstration of the principles of quantum mechanics, specifically the wave-particle duality of particles. It has been replicated numerous times and has played a crucial role in our understanding of the quantum world.

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