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Chapter 6: Q5CQ (page 223)
Your friend has just finished classical physics and can鈥檛 wait to know what lies ahead. Keeping extraneous ideas and postulates to a minimum, Explain the process of Quantum-mechanical tunneling.
Whatever you have studied under classical physics is forbidden, is allowed quantum-mechanically.
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The plot below shows the variation of 蠅 with k for electrons in a simple crystal. Where, if anywhere, does the group velocity exceed the phase velocity? (Sketching straight lines from the origin may help.) The trend indicated by a dashed curve is parabolic, but it is interrupted by a curious discontinuity, known as a band gap (see Chapter 10), where there are no allowed frequencies/energies. It turns out that the second derivative of蠅 with respect to k is inversely proportional to the effective mass of the electron. Argue that in this crystal, the effective mass is the same for most values of k, but that it is different for some values and in one region in a very strange way.
Particles of energy Eare incident from the left, where U(x)=0, and at the origin encounter an abrupt drop in potential energy, whose depth is -3E.
A beam of particles of energy E incident upon a potential step ofE is described by wave function:
A particle moving in a region of zero force encounters a precipice---a sudden drop in the potential energy to an arbitrarily large negative value. What is the probability that it will 鈥済o over the edge鈥�?
What fraction of a beam of electrons would get through a wide electrostatic barrier?
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