ECE 306
Homework Set #7
Spring 2005
(Due 12 noon, Wednesday, March 30, 2005.)
1.
Give the matrix representations of the angular momentum operators L
x
, L
y
, L
z
and
L
2
for
l
= 0, 1 and 2, in the basis in which L
z
and L
2
are diagonal.
2.
Using the matrix representations of the Cartesian components of the angular
momentum operators for
l
= 1 and 2 found in Problem 1 above, show that the
cyclic commutation relationships (6.6) and (6.7) are indeed satisfied.
3.
Since the three Cartesian components of the orbital angular momentum operators
do not commute with each other, does that mean we can never specify the three
components of the orbital angular momentum of hydrogen atom precisely
simultaneously? If that its not the case, give the conditions when they can and
cannot be specified simultaneously and why.
4.
Show that the
n
= 2,
l
= 1 and
m
l
= 1 wave function indeed satisfies the time-
independent Schroedinger’s equation given in the text for the hydrogen atom.
Show explicitly also that this wave function is normalized

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