HWork12 - Physics 344 Homework 12 Due Thursday December 2...

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Physics 344 – Homework 12 Due Thursday, December 2 Problem 1. Problem Q10S.3 from the text. Problem 2. Problems Q11.B.2 and Q11.B.3 from the text. Problem 3. Problem Q11.B.4 from the text. When discussing the electron in a metal film system in class we noted that there was a small tunneling probability for detecting an electron bound in the system outside the film. This probability decreases the more tightly bound the system is, so, we argued that in some cases it may be adequate to use the functions 0, 0 2 () s i n , 0 n x nx x xa aa π ψ < ⎛⎞ = << ⎜⎟ ⎝⎠ > as approximations to the electron-film system’s energy eigenstates. Make this approximation when solving the following problems. Problem 4. Show that the wavefunction 1 x does satisfy the time-independent Schrödinger equation within the film and, so, determine its corresponding energy eigenvalue. Use your answer to estimate the groundstate energy eigenvalue for the case of a system a = 10 nm and W = 4.08 eV that we analyzed in class. Your result should not
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