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Casimir efeect on tunneling


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In another thread (in speculations: http://www.scienceforums.net/showthread.php?t=23406 ), we were discussing the 0 point energy and tunnelling (well the thread was not specifically about that but it was a point to do with the topic).


Now neither of us has the knowledge of Quantum Mechanics to answer this properly (and it is off topic for that particular thread), so I though I'd ask here to get some clarification on it.


We were discussing electron tunnelling through a barrier. Essentially a hole in an electrically charged plate with the electrons fired at it with just enough velocity to approach the hole but not go through it so that some might tunnel through the barrier.


What we were wondering was if a Casimir resonance cavity was position so that this experiment took place inside the resonance cavity would this have any effect on the chance that an electron could tunnel through the barrier.


The reason we think it might (but as we are not sure about it I decided to ask) is that the plates, by excluding the 0 point energy would create a lower region of energy between them and therefore the electrons would not be able to "borrow" the energy from the 0 point field to make it across the barrier (tunnel).


Now I probably have the whole thing wrong, so please correct me if I do, but could the Casimir effect have an influence on tunnelling?



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I'm not aware of any experiments or discussion of this, but note that the Casimir force is very small; the excluded modes are the lowest-energy ones, since they have long wavelengths. And the "borrowing of energy" view is tied in to the classical view (where you still require that the particle go "over" the barrier) and is not actually part of the QM treatment. So even if it is a correct model, it would have an effect only for extremely small separation.

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When you talk about electron tunneling in QM fashion you would talk about it's wave function probability that a part of it can exist outside the barrier or all of it when it tunnels. To talk about borrowing energy you would then be drawing an analogy to explain it in a non QM way. I think that the electron being in a region of "low" energy has little to do with being able to borrow the energy, but it's probability of tunneling through the barrier might be lowered.

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