Transmission: Finite Potential Barriers & Potential Steps

This may appear like a homework question, but I am not asking for answers for the question, so please don't remove this post! This is a conceptual question, and I just want to show how I came to that question.

The following question, " An electron and a proton of identical energy E encounter the same finite potential barrier (E<U) For which is the probability of transmission greatest, and why?" is answered by considering the WKB approximation (below) where there is mass dependence. The obvious answer is that the electron have the highest probability of emission.

Then I encountered another question, "Calculate the fraction of 25 MeV protons reflected and the fraction transmitted for a 20 MeV step. How do your answers change if the protons are replaced by electrons?" The reflection constant reduced to the point where it is obvious that there is no mass dependence. And so the obvious answer is that the answers will not change if we changed the mass of the particle.

I wondered how transmission is different for what seems to be very similar situations.

My guess is (and this is where I need help and clarification) that because of the fact that in the first case, potential energy is greater than the particle's energy, and in the second case it is the opposite case. But how that determines whether the transmission has a mass dependence or not (respectively) eludes me.

Or is it different because we have a potential energy barrier in the first case and a potential step in the second case? This second guess is certainly very implausible according to my current understanding, because transmission just happens twice when we consider a square potential barrier (once at the first boundary, and a second at the second boundary).

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I did put up a question similar to this, but perhaps the length of the question was off-putting and inappropriate for this thread.

I am just questioning a conclusion I have drawn from some questions I have done: There are some cases when transmission can be mass dependent and some cases when it is not. Whether this is true is something I am definitely uncertain about, and if it is true, I would like to know why. Because the only the indications I have gotten about mass dependence and independence for transmission (and reflection also) are mathematical, and I am not satisfied.

DaveC426913
Gold Member
(Perhaps you shortened the question a little too much. )

Transmission of what?

Sorry, I am talking about transmission of electrons and protons through a potential barrier.

jtbell
Mentor
I did put up a question similar to this, but perhaps the length of the question was off-putting and inappropriate for this thread.
It's OK to "bump" a thread (once) after at least 24 hours. I've merged your two threads.