Chapter 6: Q9CQ (page 223)
In the wide-barrier transmission probability of equation , the coefficient multiplying the exponential is often omitted. When is this justified, and why?
It is not important for the wide barrier tunneling.
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Show that the quite general wave group given in equation (6-21) is a solution of the free-particle Schrödinger equation, provided that each plane wave's w does satisfy the matter-wave dispersion relation given in (6-23).
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.
Exercise 39 gives a condition for resonant tunneling through two barriers separated by a space width of, expressed I terms of factorgiven in exercise 30. Show that in the limit in which barrier width, this condition becomes exactly energy quantization condition (5.22) for finite well. Thus, resonant tunneling occurs at the quantized energies of intervening well.
Could the situation depicted in the following diagram represent a particle in a bound state? Explain.
What fraction of a beam of electrons would get through a wide electrostatic barrier?
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