Last time, we finished with the observation that transmission OVER a potential dip has a strange sub-case if (k2)L = n Pi! In that case, it looks like trouble, because the sin^2 in the denominator goes to zero, i.e. T -> infinity! (Impossible, T=1 is the biggest it can be!)
But we made some approximations in getting to our final result, we better go back to the start and do it right:
(Note: I made use of the fact that both terms are either +1 or -1,
but whichever, they're both identical, because they're e^(+/- i n Pi), which are the same. So I pulled it out as a common term, and squared it, making it just +1)
Bottom line: no matter what E is, or V is, if (k2)L=n Pi, then T=1!
This is a special resonance phenomenon. The well has become invisible! It's like it's not even there! The quantum particles behave "classically", sort of. Why is this? Inside the well,
In words, an integer number of half wavelengths FITS in the well. In this case, all the reflected waves end up destructively interfering, and all the transmitted waves add up. Remember light entering a thin film, in Physics 1120? It's the exact same story!
If
,
then the first reflection and the double reflection differ by exactly one
wavelength.
But, there's also a phase flip at the first boundary, and so these waves destructively interfere, and you get no reflection. It's the basis for "non glare" glass coatings! With light, it only works for one particular color (for any given thickness), and in our quantum case, we're talking about incident waves of some given (fixed) momentum, which is also "monochromatic".
This phenomenon was first seen experimentally in the 1920's. We'll talk about it next time.
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