Chem 110A
MQII_2009
1
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Second Midquarter Exam – November 25, 2009
Chemistry 110A
Professor McCurdy
Instructions: You may use only a pencil or pen. You may have one sheet of equations
that you have prepared yourself. No other materials are allowed. Write all answers on the
exam in the spaces provided, or clearly continued on the backs of the pages and labeled
unambiguously.
There are three pages of equations distributed with the exam.
Be sure to look at them
before
you begin the exams.
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Chem 110A
MQII_2009
2
1. (30 points) (
Problem 822) The total spin angular momentum operator for a two
electron system is
ˆ
S
z
,
total
=
ˆ
S
z
1
+
ˆ
S
z
2
Show that
!
(1,2)
=
1
2
1
s
"
(1)
1
s
#
(1)
1
s
"
(2)
1
s
#
(2)
is an eigenfunction of
ˆ
S
z
,
total
, and give the
eigenvalue
associated with it. (
The notation
1
s
"
(1)
means
"
1
s
(
r
1
)
#
(1)
where
"
1
s
(
r
1
)
is a 1s orbital
)
We start by writing the LHS of the eigenvalue equation
ˆ
S
z
,
total
"
(1,2)
=
ˆ
S
z
1
+
ˆ
S
z
2
(
)
1
2
1
s
#
(1)
1
s
$
(1)
1
s
#
(2)
1
s
$
(2)
=
1
2
ˆ
S
z
1
+
ˆ
S
z
2
(
)
1
s
#
(1)1
s
$
(2)
%
1
s
#
(2)1
s
$
(1)
(
)
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 Spring '10
 Phillips
 Angular Momentum, ground state, $ 1, Chem 110A

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