Electrons traversing a Potential well

In summary, in a one dimensional world with a potential well near x=0 and free electron states at x=+inf or -inf, the transmission coefficient for an electron arriving at the well from x=-inf and the transmission coefficient for an electron traveling in the opposite direction should be equal if the potential well is symmetric. This is because the system's Hamiltonian is symmetric under parity, meaning the electron cannot differentiate between the two directions. However, if the potential well is not symmetric, then the transmission coefficients may not be equal.
  • #1
Let's imagine an electron that lives in an one dimensional world where there is a potential well near x=0 and that for x=+inf or -inf the electron is free.
Is there any relation between the transmission coefficient of an electron arriving at the well coming from x=-inf and the transmission coefficient for another electron traversing the other way?
Should they be equal?
 
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  • #2
If the potential well is symmetric, then it means the entire Hamiltonian is symmetric under parity (space reversal). So there's nothing in the description of the system that could allow the electron to know which direction it's coming from. In that case, the coefficient of transmission should be the same either way.
 
  • #3
it is not symmetric
 

What is a Potential Well?

A potential well is a region in space where the potential energy of a particle is lower than its surroundings, causing the particle to be trapped in the well.

How do electrons traverse a Potential Well?

Electrons can traverse a potential well through the process of tunneling, where they are able to pass through energy barriers even if they do not have enough energy to overcome them.

What factors affect the traversal of electrons through a Potential Well?

The size and shape of the potential well, as well as the energy and momentum of the electrons, can affect their traversal through the potential well.

What are the applications of studying Electrons traversing a Potential Well?

Understanding the behavior of electrons in potential wells is important in various fields such as semiconductor devices, quantum computing, and nanotechnology.

How is the traversal of electrons through a Potential Well related to quantum mechanics?

The behavior of electrons in potential wells is governed by the principles of quantum mechanics, specifically the wave-like nature of particles and the concept of probability. This understanding is crucial in many modern technologies.

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