MSE 310/ECE 340
Dept. of Materials Science & Engineering
Electrical Properties of Materials
Fall 2011/Bill Knowlton
1
Problem Set 4
(Show all work for all problems)
1.
In class, we considered the radial wave function of an electron in a hydrogen atom given by:
o
r
a
re
a.
Explain the symmetry (i.e., geometry) that the electron experiences. That is, if you were to normalize the
wave function, what coordinate system would you use? Explain.
b.
Using part
a
, normalize the wave function. That is, find the normalization constant and provide the
normalized wave function.
2.
The Heisenberg uncertainty principle is given by:
2
x
xp
where
Δ
x
and
Δ
p
x
are given by expectation values of
x
and
p
x
. Specifically, they are given by:
2
2
2
2
ˆˆ
and
xx
x
xxx
p
pp
For the particle in the box problem, determine the
Heisenburg Uncertainty Principle
by finding each
expectation value separately. That is:
a.
Find
x
. Simplify your answers as much as possible. Note: you will need to normalize the wave
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This note was uploaded on 10/16/2011 for the course ENGINEERIN MSE 310 taught by Professor Billknowlton during the Spring '10 term at Boise State.
 Spring '10
 BillKnowlton

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