Now we have a step potential

In summary, the conversation discusses the calculation of k in a simple situation like a step potential, where k=sqrt(2m*abs(E-V))/hbar. The question arises of what happens when the energy of the approaching electron is equal to the potential, E=V. This results in k being equal to zero, indicating that there is a zero probability of the electron penetrating the barrier. However, the finite barrier still has a chance of being penetrated, as opposed to an infinite barrier. It is also mentioned that there are no stationary states, only scattering states.
  • #1
joe2005
2
0
I am taking a course in solid state electronics at the university and I was thinking about one detail in the calculation of k. In a simple situation like a step potential we say that k=sqrt(2m*abs(E-V))/hbar . Now my question is What happens if the electron approaching the barrier is having an energy E=V. According to the formula k will be zero. Does that me that the electron will not "move" in the barrier. Is (E=V) a resemblence of the infinite potential case but at a single E value?

Thanks...
 
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  • #2
If you are taking a course in solid state physics you should have covered this in a previous course. " Is (E=V) a resemblence of the infinite potential case but at a single E value?" I haved no idea what you mean by that but: FINITE is not the same as INFINITE! Unless your step is to an "infinite" potential, you have a finite potential and there is a probability that the electron will penetrate the potential step. If I remember correctly the standard method of solving the differential equation, to determine what that probability is, is the "WKB" approximation.
 
  • #3
Sorry if I wasn't clear. What I meant is that if at E=V our k=0 and the electron has a zero chance of penetration then this means that at this specific case the "FINITE" barrier will acts as an "INFINITE" one from the point of view of that electron having E=V...
 
  • #4
There are no stationary states, if that's your question. There are only scattering states, like with a free particle.
 

1. What is a step potential?

A step potential, also known as a potential barrier, is a sudden change in potential energy that occurs in a physical system. It can arise in many different situations, such as when a particle encounters a sudden change in potential energy due to a barrier or a well.

2. How does a step potential affect the behavior of particles?

A step potential can significantly alter the behavior of particles by changing their energy levels and momentum. When a particle encounters a step potential, it can either reflect off the potential barrier or tunnel through it, depending on its energy and the height of the barrier. This can have significant implications in quantum mechanics, where particles can exhibit wave-like behaviors and can tunnel through potential barriers.

3. What factors influence the height of a step potential?

The height of a step potential is influenced by several factors, including the strength of the potential barrier, the energy of the particles, and the distance between the particles and the barrier. A higher potential barrier will make it more difficult for particles to pass through, while a lower barrier will allow for more particles to pass through.

4. How does a step potential affect the transmission of particles?

The transmission of particles across a step potential depends on the energy of the particles and the height of the barrier. If the energy of the particles is higher than the barrier, they are more likely to tunnel through it and transmit to the other side. However, if the energy is lower than the barrier, the particles are more likely to be reflected and not transmit through the potential barrier.

5. What are some real-world applications of a step potential?

Step potentials have numerous applications in various fields of science, including quantum mechanics, semiconductor devices, and nuclear physics. In quantum mechanics, they are used to study the behavior of particles and their energy levels. In semiconductor devices, step potentials are used to control the flow of electrons, which is crucial in modern electronic devices. In nuclear physics, step potentials are used to study the behavior of nucleons in nuclear reactions.

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