# Can an electron quantum tunnel inside the potential barrier?

Leonardo Muzzi
TL;DR Summary
When I see explanations for quantum tunneling, the discussion is around the probability of an electron manifesting itself before the potential barrier, and after the potential barrier. However, looking at the curves draw, there is a non-zero probability (the evanescent part of the wave) inside the potential barrier itself. Does that mean the electron can be located inside the barrier? What is the possible physical interpretation for that?
When I see explanations for quantum tunneling, the discussion is around the probability of an electron manifesting itself before the potential barrier, and after the potential barrier. However, looking at the curves draw, there is a non-zero probability (the evanescent part of the wave) inside the potential barrier itself. Does that mean the electron can be located inside the barrier? What is the possible physical interpretation for that?

Staff Emeritus
Summary:: When I see explanations for quantum tunneling, the discussion is around the probability of an electron manifesting itself before the potential barrier, and after the potential barrier. However, looking at the curves draw, there is a non-zero probability (the evanescent part of the wave) inside the potential barrier itself. Does that mean the electron can be located inside the barrier? What is the possible physical interpretation for that?

When I see explanations for quantum tunneling, the discussion is around the probability of an electron manifesting itself before the potential barrier, and after the potential barrier. However, looking at the curves draw, there is a non-zero probability (the evanescent part of the wave) inside the potential barrier itself. Does that mean the electron can be located inside the barrier? What is the possible physical interpretation for that?

Well, what is the problem with the tunneling electron being located inside the barrier as the "physical interpretation"?

There have been quite a few threads on this topic, and this was one of my responses:

Zz.

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Leonardo Muzzi
Leonardo Muzzi
Leonardo Muzzi
Well, what is the problem with the tunneling electron being located inside the barrier as the "physical interpretation"?

There have been quite a few threads on this topic, and this was one of my responses:

Zz.

OK I understood that explanation. Which brings another question: if the particle can in fact resolve inside the barrier, that probability exists regardless of the with of the barrier. Does that mean that particles can tunnel inside any barrier, regardless of the size of it? Let's say there is an infinite long barrier and the probability amplitude on the other side is zero. The particle could still resolve itself inside the barrier. Would that reasoning be correct?

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OK I understood that explanation. Which brings another question: if the particle can in fact resolve inside the barrier, that probability exists regardless of the with of the barrier. Does that mean that particles can tunnel inside any barrier, regardless of the size of it? Let's say there is an infinite long barrier and the probability amplitude on the other side is zero. The particle could still resolve itself inside the barrier. Would that reasoning be correct?
If the barrier is "infinitely" long then there is no other side.

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2022 Award
Staff Emeritus
OK I understood that explanation. Which brings another question: if the particle can in fact resolve inside the barrier, that probability exists regardless of the with of the barrier. Does that mean that particles can tunnel inside any barrier, regardless of the size of it? Let's say there is an infinite long barrier and the probability amplitude on the other side is zero. The particle could still resolve itself inside the barrier. Would that reasoning be correct?

You need to define what you mean by "resolve". I believe that I didn't use such a word.

Please note that I tried to be careful in the response that I wrote then. I simply stated that this observation is consistent with the idea that the electron did pass through the barrier, and that it didn't just disappear on one side and appeared at the other side. However, the nature of what it was doing while inside the barrier is still debatable. So I am hesitant to agree with the claim that it can be "resolved" inside the barrier.

Also note that the probability that it can penetrate into the barrier drops exponentially as you go further into the barrier. If you make the barrier thick enough, there will be no appreciable tunneling. So I don't quite understand that part of your question. The wavefunction doesn't propagate without attenuation inside the barrier.

Zz.

vanhees71 and PeroK
OCR
If the barrier is "infinitely" long then there is no other side.

Lol. . . well now, that's simply a one sided statement . . . .

.

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