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I am picturing a sine wave acting as a barrier for my quantum tunneling experiment, it can be an electric field etc. Now I have an electron whereby a portion of its probability intersects and even crosses over the sine wave (barrier) so there should be a possibility of finding the electron there, so far so good. But suppose both waves interfere with each other constructively creating a bigger wave and then resume their original size upon exit, there is a possibility that the peak of the electron wave jump (overlapping) across the barrier much faster than speed of light no? I don't know how speed is calculated using waves but I believe the leading part of the wave (electron) can actually leaps across faster if the sum of the constructive wave is more bigger right?

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I’m not sure I understand your question, but if I did:

A time varying electric field is simply that. It does not contain electron waves. Rather, it is simply an electric field that changes its direction as a function of time. In this sense, it is not a wave physically even though if you did plot the function say

$$E = E_0 \sin(kx - \omega t)$$

you would get a graph similar for the wave function

$$\psi \propto e^{i(kx- \omega t)}$$

But this does not mean that they both represent the same physical phenomena, and so will not “superpose” to form another “wave”.

Also, I have never come across a quantum tunneling problem with an oscillating barrier.

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  • $\begingroup$ Time varying barrier problems do show up, but they tend to be messy since now energy and even what Hilbert space one is in changes over time. The infinite square well with a linearly moving side is a classic example. Non-infinite time-dependent barriers with tunnelling sounds like they only rarely have analytic solutions. $\endgroup$ – Anders Sandberg Jan 9 at 9:37

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