Physics 486 FA07
Homework Set 4
Due: Sep 27, 2007
1)
Based on Griffiths 2.37
. An electron in an infinite square well potential occupying the
region 0
≤
x
≤
L has the initial wavefunction
Ψ
(x,0) = A sin
3
(
π
x/L) within the same region.
(a) Determine the constant A.
Hint: sin
m
α
and cos
m
α
can be reduced by repeated application of trigonometric sum
formulas to linear combinations of sin(n
α
) and cos(n
α
), n=0,1,2,3.
.
(b) Find the timedependent wavefunction
Ψ
(x,t).
(c) What is the expectation value of position ‹x› as a function of time?
(d) What is the expectation value of the energy in terms of the ground state energy E
1
?
If the length of the well is L = 3nm, what is the value of this expectation in electron volts?
(e) If a measurement is made on the energy of the particle, what are/is the possible outcome(s)
and with what proability/ies?
2)
Momentum representation.
In last week’s homework, you considered an electronic wavefunction
given by
ψ
(x)=N/(x
2
+a
2
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 Fall '08
 Staff
 Work, Quantum Physics, 2m, J2, 3nm, momentum representation

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