PHYS 507
Homework VIII (Fall ’05)
Assigned:
December 14, 2005, Wednesday.
Due:
December 21, 2005, Wednesday, at 5:00 pm.
1.
Let
~
J
=
~
J
1
+
~
J
2
be the total angular momentum of two independent systems. Suppose
the quantum numbers for
J
2
1
and
J
2
2
are
j
1
and
j
2
respectively and we consider the
states for which
J
2
is quantized with quantum number
j
. In this case all of these three
vectors
~
J
1
,
~
J
2
and
~
J
have known magnitudes but has uncertain orientations. Despite
the uncertainty in orientation, these three vectors form a triangle and we can talk
about definite values of the angles in this triangle. Physically, we tend to interpret the
maximum
j
value (
j
=
j
1
+
j
2
) as corresponding to states where the vectors
~
J
1
and
~
J
2
are more or less parallel to each other. Similarly, minimum
j
value (
j
=

j
1

j
2

)
corresponds to states where these vectors are more or less antiparallel to each other.
(a)
Consider the particular case
j
1
= 2 and
j
2
= 1. Compute the angle between
~
J
1
and
~
J
2
for each possible value of
j
.
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 Spring '11
 starg
 Angular Momentum, total angular momentum

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