A quantum particle can tunnel through a barrier and we can describe why this is so by the uncertainty principle. However, there is something I want to clarify about the reasoning behind this.(adsbygoogle = window.adsbygoogle || []).push({});

I believe the argument goes like this: Imagine the quantum particle never entered the barrier and we know for sure it is in the classically permissible area. Then we know Δx = 0 which implies Δp →∞. (Only allowed for infinite potential wells). Hence the original assumption that the particle was never in the barrier is false and thus some of the probability wave must leak in to the barrier. That is why we know quantum tunneling is possible.

What I don't understand, however, is even if we assume the particle can never enter the barrier and we know it is still outside it, then why does this imply Δx = 0?

As a friend of mine said: If I know my keys aren't in my pocket, that does not tell me exactly where they are..

I understand the above anology is obviously very different from the quantum world, but the question still remains for me: why does Δx = 0? Even if we know the particle is outside the barrier, surely it can still be anywhere so why does this automatically imply Δx =0?

Thanks for any input.

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# Quantum Tunneling: Particle location

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