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

[joe2005]

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...

 

[HallsofIvy]

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.

 

[joe2005]

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...

 

[rachmaninoff]

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