Physics 486 FA07
Homework Set 3
Due: Sep 20, 2007
1)
Expectation values
. The wavefunction of an electron confined to a particular potential V(x)
is given by
ψ
(x)=N/(x
2
+a
2
), where N and a are constants.
(a) Sketch this wavefunction as a function of x.
(b) Find the normalization constant N.
(c) Find the expectation value of the position operator x.
(d) Find the expectation value of the momentum operator p.
(e) Find the expectation value of the operator x
2
.
2)
Infinite Square Well Wavefunction
. A particle of mass m is confined in the infinite square well
potential extending from x = 0 to x = L.
At t = 0, the wavefunction of the particle is given by:
Ψ
(x,0) = Nsin(2
π
x/L)
0 <
x <
L/2
Ψ
(x,0) = 0
elsewhere
(a)
Sketch the wavefunction at t = 0.
(b)
Find the normalization constant, N.
(c) Is this wavefunction an eigenstate of the timeindependent SEQ for this potential?
Please
briefly justify your answer.
(d) Write the wavefunction
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 Fall '08
 Staff
 Work, Quantum Physics, expectation value, 12 cm, onedimension

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