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Extra resources for Advanced quantum mechanics

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These electrons arrive at the back of the screen perpendicular to the surface. , like a cathode ray tube screen) is placed 10 cm away from the other side of the screen and parallel to it. , the distance between the centers of the bright stripes)? (ii) What is the period of the stripes if we use protons (hydrogen nuclei) instead of electrons? , the wave is propagating perpendicularly to the screen). Presume that we take the simple “Huygens’ principle” model of diffraction, and, as above model the slit as a source of a spherically expanding (complex) wave (and hence each vertical line in the slit is a source of a circularly expanding wave).

We presume that F = 0 . Otherwise the wave amplitude would increase exponentially to the right for ever, which does not appear to correspond to any classical or quantum mechanical behavior we see for particles incident from the left. 43) Even this solution is strange. It proposes that the wave inside the barrier is not identically zero, but rather falls off exponentially as we move inside the barrier. 39). 38), gives us C−D= Addition of Eqs. 45) gives us 27 Formally B = C + D, A = - i(C – D). 46) Subtraction of Eqs.

The behavior of a quantum mechanical particle at a potential barrier is quite different. As we shall see, it both can be found within the barrier and can get to the other side of the barrier, even if its energy is less than the height of the potential barrier. We start by considering a barrier of finite height, Vo, but of infinite thickness, as shown in Fig. 3. For convenience, we choose the potential to be zero in the region to the left of the barrier (it would not matter if we chose it to be something different, since only energy differences actually matter in these kinds of quantum mechanical calculations).

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