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Firstly, the transmission is always between zero and one, and there are some sweet spots where it is one exactly so in between two sweet spots it has to decrease then increase again. But that's a bit uninformative and uneducational. And you asked about why, so let's look at the why of tunneling and quantum dynamics in general. You start with a wave packet ...


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The transmission probability depends on the relation between the barrier width and the de Broglie's wavelength of the electron (within the barrier). The waves reflected from the front and the end of the barrier interfere constructively or destructively depending on this relation. The description of a similar phenomenon for light can be found, e.g., at ...


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I) Recall that the probability current is $$\tag{1} J(x)~:=~\frac{i\hbar}{2m}W(\psi,\psi^{\ast}) (x), $$ where $$\tag{2} W(\psi,\psi^{\ast}) (x)~:=~\psi(x) \psi^{\prime}(x)^{\ast}- \psi^{\prime}(x)\psi(x)^{\ast}$$ is the Wronskian. Unitarity of the $S$-matrix is equivalent to the statement that $$ \lim_{x\to -\infty} W(\psi,\psi^{\ast}) ...


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I like and upvoted the accepted answer, so my adding this (partial) answer is only to add a short and intentionally non-mathematical view to the answer. I find this a genuinely intriguing question that I think with some effort could be answered well in terms that are a lot less mysterious sounding. This answer is not that, but it is perhaps a start... ...


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One way to look at quantum mechanics is through the dynamics. One way to look at the dynamics is through the Schrödinger equation and there is nothing wrong with that. Since it is a linear equation it does encourage one to look at particular solutions and then make a general solution as a simple sum of those solutions, which can sometimes delay ...


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The probability of just one of your atoms getting through the wall is very low, multiply that probability (which is way lower than 1) by the probabilty that all of your atoms go through, you get a number so small that the universe would almost certainly have ended long before you got through the wall. A 70 Kg human body has approximately 7 X $10^{27}$ ...


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Stars are a great example. Quantum tunneling is basically just getting over an energy barrier that is unpenetrable in classical mechanics. Stars survive off of this phenomena. Stars usually do not have enough energy to fuse hydrogen into helium. The hydrogen atoms (a small percent, but since there are so many atoms, it matters) tunnel over the energy ...



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