[題目] a half infinite well
這是近物的一題:
A half-infinite well has an infinitely high wall at the origin and
one of finite height U0 at x=L. Like the finite well, the number
of allowed states is limited.
(a) Assume that it has two states, of energy E1 and E2, where
E2 is not much below U0. Make a sketch of the potential
energy, and then add plausible sketches of the two allowed
wave functions on separate horizontal axes whose heights
are E1 and E2. (10 points)
(b) Show that there is no bound state unless U0 is at least
h2/32mL2. (Hint: What is the maximum wavelength possible
within the well?) On the other hand, a finite well always has
at least one bound state. Why? (10 points)
(c) Obtain the energy quantization condition as a function of E.
(10 points)
(d) Find the two bound-state energies for a well in which
U0=h2/2mL2. Compare the results to the infinite well and
comment. (10 points)
老師只教我們infinite&finite 沒有教這種一半是infinite一半是finite
不曉得版大有人可以教我嗎?
謝謝謝謝
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