# Dynamics of the double slit experiment

• B
• gerald V
In summary, the double slit setup is arranged so that the screen is in a fixed plane while the apparatus is perpendicular to the screen. When considering the dynamics of a single electron, it is important to take into account the state in which the electron is prepared. When using the double slit experiment to demonstrate quantum behavior, interference fringes can be observed when the partial waves from each slit overlap. The meaning of this interference is that the probability density of the electron's position is described by the wave function. This can be seen by repeating the experiment with many equally prepared single electrons and observing the distribution of dots on the screen. For more information on this topic, see the beginning of the Feynman Lectures, vol. III.
gerald V
The spatial orientation of the double slit setup be so that the screen extends in a plane ##x = constant##, while the entire apparatus sits on a ray perpendicular to the screen (of course, the slits sit and extend a bit off this ray).

My questions are about the dynamics in x-direction if only a single electron is involved. Is this more or less classical? That is: Makes it sense to say that the electron is emitted at a specific point in time (or how large is the uncertainty), and can this point in time be determined? The same for the impact of the electron on the screen? Can the flying time from emission from the source to impact on the screen be computed and/or measured and if yes, how does it depend on the diffraction angle?

Thank you in advance!

It depends on the state the electron is prepared in. The usual point of the double-slit experiment is however to demonstrate quantum behavior, and you describe an incoming electron running with a very well determined momentum perpendicular to the slits towards the slits (you can take a plane wave as an idealization). Then you solve the Schrödinger equation, using Huygens's principle, which leads to interference of the partial waves originating from each of the slit, i.e., if you look far enough from the slits, in the region, where these two partial waves overlap, you get interference fringes for the matter waves.

The meaning however is that the ##|\psi(x)|^2## is the position probability density for a single electron, i.e., each single electron running through the slits and hitting the screen will leave a single dot there. Repeating the experiment with very many equally prepared single electrons leads to a distribution of the dots given by the probability distribution predicted by the wave function.

For an excellent discussion of this issue, see the beginning of the Feynman Lectures, vol. III:

http://www.feynmanlectures.caltech.edu/III_01.html

BvU

## 1. What is the double slit experiment?

The double slit experiment is a fundamental experiment in quantum mechanics that demonstrates the wave-particle duality of matter and the concept of superposition. It involves passing a beam of particles, such as electrons or photons, through two parallel slits and observing the resulting interference pattern on a screen.

## 2. What is the significance of the double slit experiment?

The double slit experiment is significant because it challenges our classical understanding of particles as discrete and localized objects. It suggests that particles also have wave-like properties and can exist in multiple states simultaneously. This experiment has had a major impact on the development of quantum mechanics and our understanding of the nature of reality.

## 3. How does the double slit experiment demonstrate wave-particle duality?

The double slit experiment demonstrates wave-particle duality by showing that particles can behave like waves and exhibit interference patterns. When a beam of particles is passed through the two slits, they diffract and interfere with each other, creating a pattern of light and dark bands on the screen. This behavior is characteristic of waves, but individual particles are also detected at specific points on the screen, showing their particle-like nature.

## 4. What are some variations of the double slit experiment?

There are several variations of the double slit experiment, including the delayed choice experiment, the quantum eraser experiment, and the entanglement swapping experiment. These variations involve adding additional components, such as detectors or entangled particles, to further explore the behavior of particles and the role of observation in quantum mechanics.

## 5. What implications does the double slit experiment have for our understanding of reality?

The double slit experiment challenges our classical understanding of reality and suggests that the act of observation can affect the behavior of particles. This has led to various interpretations of quantum mechanics, such as the Copenhagen interpretation and the many-worlds interpretation. The double slit experiment also has implications for fields such as quantum computing and quantum communication, which rely on the principles of superposition and entanglement.

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