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Chapter 6: Q16E (page 224)
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 “go over the edge”?
I will definitely reflect for tending to infinite.
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The matter wave dispersion relation given in equation (6-23) is correct only at low speed and when mass/internal energy is ignored.
(a) Using the relativistically correct relationship among energy, momentum and mass, show that the correct dispersion relation is
(b) Show that in the limit of low speed (small p and k) and ignoring mass/internal energy, this expression aggress with that of equation (6-23).
From equations (6-23) and (6-29) obtain the dispersion coefficient for matter waves (in vacuum), then show that probability density (6-35) follows from (6-28)
What fraction of a beam of electrons would get through a wide electrostatic barrier?
The diagram below plots ω(k) versus wave number for a particular phenomenon. How do the phase and group velocities compare, and do the answer depend on the central value of k under consideration? Explain.
Suppose the tunneling probability isfor a wide barrier when E is
(a) About how much smaller would it be if ’E’ were instead ?
(b) If this case does not support the general rule that transmission probability is a sensitive function of E, what makes it exceptional?
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