PHY3063 Spring 2007
Problem Set 8
Department of Physics
Page 1 of 3
PHY 3063 Problem Set #8
Due Tuesday April 24 (in class)
(Total Points = 105)
Reading:
Read Tipler & Llewellyn Chapter 7.
Problem 1 (20 points):
The Pauli spin matrices are given by
=
0
1
1
0
x
σ
−
=
0
0
i
i
y
σ
−
=
1
0
0
1
z
σ
(a) (10 points)
Show that
σ
↑
i
=
σ
i
, det(
σ
i
) = 1, Tr(
σ
i
) = 0, [
σ
i
,
σ
j
] = 2i
ε
ijk
σ
k
, and {
σ
i
,
σ
j
} = 2
δ
ij
.
Note that [A, B] = AB – BA and {A, B} = AB +BA.
(b) (10 points)
Show that
∑
+
=
l
l
ijl
ij
j
i
i
σ
ε
δ
σ
σ
.
Problem 2 (20 points):
Quarks and antiquarks carry spin ½.
(a) (10 points)
Three quarks bind together to form a baryon (such as a proton or a neutron).
What are the possible spin states for a baryon (assuming that the quarks are in the ground state so
that the orbital angular momentum is zero).
(b) (10 points)
A quark and antiquark bind together to form a meson (such as a
π
meson).
What are the possible spin states for a meson (assuming that the quarks are in the ground state so
that the orbital angular momentum is zero).
Problem 3 (10 points):
Evaluate the following in SU(2).
(a) (1 point)
2 × 1 =
(b) (1 point)
2 × 2 =
(c) (1 point)
3 × 2 =
(d) (1 point)
3 × 3 =
(e) (1 point)
5 × 2 =
(f) (1 point)
5 × 3 =
(g) (1 point)
4 × 2 =
(h) (1 point)
2 × 2 × 2 =
(i) (1 point)
2 × 2 × 3 =
(j) (1 point)
3 × 3 × 3 =
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 Spring '07
 Field
 Physics, ground state, Department of Physics

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