As we see in Figures 10.23, in a one-dimensional crystal of finite wells, top-of-the-band states closely resemble infinite well states. In fact, the famous particle-in-a-box energy formula gives a fair value for the energies of these states and thus the energies of the bands to winch they belong, (a) If for n in that formula you use the number of antinodes in the whole wave function, what would you use for the box length L,? (b) If, instead, the n in the formula were taken to refer to band n could you still use the formula? If so, what would you use for L? (c) Explain why the energies in a band do or do not depend on the size of the crystal as a whole.
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