What is the maths behind single electron double slit interference please?

In summary, single electron double slit interference is a phenomenon where a single electron passing through two parallel slits creates an interference pattern. This is due to the wave-like nature of electrons, which creates a pattern when the electron passes through the slits and interferes with itself. The mathematical explanation for this phenomenon involves using the Schrödinger equation and understanding the wave-particle duality of electrons. While this phenomenon is not observable in everyday life, it is important in understanding quantum mechanics and has practical applications in fields such as electronics and computing.
  • #1
alfredblase
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Basically I'm looking to find a mathematical treatment of the single electron double slit interference phenomenom,, presumably someone has already done the maths for it but I can't seem to find it,, can you point me to an article, paper or book which has it? [preferably online]

Thanks a lot =)
 
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  • #2
It is essentially the same as the optical case (but with an adapted dispersion relation).
 
  • #3

1. What is single electron double slit interference?

Single electron double slit interference is a phenomenon where a single electron passing through two parallel slits creates an interference pattern on a screen behind the slits. This pattern is similar to the pattern created by light passing through double slits.

2. How is the interference pattern created?

The interference pattern is created due to the wave-like nature of electrons. As the electron passes through the slits, it diffracts and spreads out, creating a wave-like pattern. When these waves from the two slits overlap, they interfere with each other, creating the observed pattern.

3. What is the mathematical explanation for this phenomenon?

The mathematical explanation for this phenomenon is based on the principles of quantum mechanics. It involves using the Schrödinger equation to describe the behavior of the electron as a wave function, and then using this wave function to calculate the probability of the electron being detected at a specific location on the screen.

4. Why is this phenomenon important in quantum mechanics?

Single electron double slit interference is important in quantum mechanics because it demonstrates the wave-particle duality of electrons. It shows that particles, such as electrons, can exhibit both wave-like and particle-like behavior, which is a fundamental concept in understanding the behavior of matter at the quantum level.

5. Can this phenomenon be observed in everyday life?

No, single electron double slit interference is not observable in everyday life. It can only be observed in controlled laboratory conditions using specialized equipment. However, the principles behind this phenomenon are important in understanding the behavior of matter at the quantum level, which has practical applications in fields such as electronics and computing.

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