What Happens When the Electron Energy E Equals Potential V in Quantum Mechanics?

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Discussion Overview

The discussion revolves around the behavior of an electron approaching a potential barrier in quantum mechanics, specifically when the electron's energy E equals the potential V. Participants explore implications for the wave number k and the electron's ability to penetrate the barrier, considering both finite and infinite potential scenarios.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that when E equals V, the formula for k results in zero, leading to questions about the electron's movement within the barrier.
  • Another participant emphasizes that a finite potential is not equivalent to an infinite potential, suggesting that there remains a probability for the electron to penetrate the barrier.
  • A later reply clarifies that at E=V, while k is zero, it implies that the finite barrier behaves like an infinite barrier for the electron in terms of penetration probability.
  • One participant states that there are no stationary states in this scenario, only scattering states akin to those of a free particle.

Areas of Agreement / Disagreement

Participants express differing views on the implications of E=V, with some arguing that it leads to a zero probability of penetration, while others contend that finite potentials still allow for some probability of penetration. The discussion remains unresolved regarding the exact nature of the electron's behavior at this energy condition.

Contextual Notes

Participants reference the WKB approximation as a method for determining penetration probability, but the discussion does not resolve the mathematical implications or assumptions underlying the scenario.

joe2005
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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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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.
 
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...
 
There are no stationary states, if that's your question. There are only scattering states, like with a free particle.
 

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