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Yes, the two are intimately related. One way, as in QMechanic's answer, is via Wick rotations, but in general there is a lot more freedom once you allow integration contours to go over into the complex plane. In my area, strong field physics, the use of complex time to understand tunnelling problems is everyday bread and butter for many people, and it is the ...


6

Yes, quantum tunnelling in the double well potential can be solved in a Wick-rotated Euclidean formulation $$ S_E[x]~=~\int \! dt_E \left[ \frac{1}{2}\left(\frac{dx}{dt_E}\right)^2 - (-V) \right], $$ see e.g. Ref 1. Here $t_E=it_M$ denotes Euclidean time. The Euclidean action is in turn interpreted as the usual kinetic minus potential term with a potential ...


1

In quantum mechanics velocity is not an easy concept. Here particle motion is replaced by a wave. Momentum, is easier to define in quantum mechanics. A complex wave $\exp(ikx)$ describes a particle with momentum $p=\hbar k$ where $\hbar$ is Plancks constant divided with $2\pi$. It is fundamental in quantum mechanics that momentum cannot strictly be defined ...


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There are numerous applications of quantum tunnelling. A few that pop in my mind right now are: Radioactive decay: Particles tunnel out of the nucleus of which they are bounded by a potential. Classically this is forbidden as the nucleus is very strongly being held together by strong nuclear forces. Scanning tunneling microscope: A scanning tunneling ...



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