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24. Electronpositron pairs are emitted in a decay process (moving in opposite directions) in a spin state

0
,
0
i
spin
=

s, m
i
of zero total spin angular momentum
~
S
=
~
S
1
+
~
S
2
.
(a) What is the mean value that will be obtained in a measurement performed on an ensemble of such
electronpositron pairs of the operator
S
1
z
S
2
z
? Is the value the same as that which one would obtain
by independently measuring the values of
S
1
z
and of
S
2
z
and forming the product of the mean values
of each? Explain.
(b) What is the mean value that will be obtained in a measurement performed on an ensemble of such
electronpositron pairs of the operator
S
1
x
S
2
x
? (Feel free to use any appropriate symmetry argument.)
(c) If the operator
~
S
1
·
~
S
2
is measured on this state, what values can be obtained, and with what probability
will they occur?
25. Consider two identical particles that are in states of total angular momentum
j
in the direct product space
S
(
j
1
,j
2
)=
S
(
j
1
)
×
S
(
j
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This note was uploaded on 12/19/2010 for the course PHYSICS ph 463 taught by Professor Paule. during the Fall '10 term at Missouri S&T.
 Fall '10
 PaulE.
 mechanics, Angular Momentum, Momentum, Work

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