Keeping extraneous ideas and postulates to a minimum,
How can we explain the process of quantum-mechanical tunneling?
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3$\begingroup$ I don't understand the question. Quantum mechanics has a simple explanation for tunneling, so what is the problem? $\endgroup$– MartinCommented Apr 15, 2015 at 15:36
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$\begingroup$ This is informative azoquantum.com/Article.aspx?ArticleID=12 $\endgroup$– anna vCommented Apr 15, 2015 at 16:43
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$\begingroup$ The notion of tunneling is based on thinking of particles as little balls with specific position. If we remember that this picture is wrong and that matter is wave-like, tunneling is understood as the spread-outedness of those waves following by interaction with another system which forces the particle to (sometimes!) localize into a specific location. $\endgroup$– DanielSankCommented Apr 15, 2015 at 16:46
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$\begingroup$ I have voted to reopen because I feel the question can be answered in a way that is beginner-accessible but not (too) misleading. $\endgroup$– John RennieCommented Apr 16, 2015 at 17:03
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1 Answer
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Its simple enough. If classical particles encounter a potential step higher than their kinetic energy they cannot penetrate it. Because as soon as they penetrate the barrier they will have a negative kinetic energy, which is not possible.
A wave reacts differently to potential barriers. Waves don't stop abruptly at finite potential barriers. Instead they decay exponentially in such a region. Now, you may wonder why should a wave be able to penetrate a barrier (even to a limited extent) when a particle cannot.(This I cannot answer intuitively. All I can say is that the wave equation admits decaying solutions inside the barrier, and so they can penetrate it).
But aside from that everything is clear. Since a quantum particle acts as a wave, it will have a wavefunction (which is basically a solution to a wave equation) that is decaying exponentially within the barrier. But what if the barrier is so thin that the wavefunction cannot decay to zero before reaching the other end? Then of course, the particle's wavefunction will be non-zero outside the potential barrier and there will be a probability to detect the particle outside the barrier. And hence tunneling.