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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 electronfilm system’s energy eigenstates. Make this
approximation when solving the following problems.
Problem 4.
Show that the wavefunction
1
x
does satisfy the timeindependent
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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This note was uploaded on 11/26/2010 for the course PHYS 344 taught by Professor Garfinkel during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 Garfinkel
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