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Homework 4
PHZ 3113
Due Monday, February 8, 2010
Chapter 3
1. The Pauli matrices below are related to the spin of a spin 1
/
2 particle
σ
x
=
±
0 1
1 0
²
σ
y
=
±
0

i
i
0
²
σ
z
=
±
1
0
0

1
²
a) Show that the Pauli matrices are unitary
and
Hermitian
b) Find the eigenvectors and eigenvalues, and the unitary transformation matrix
U
and
U
†
for
σ
x
and
σ
y
. Note that
σ
z
is already diagonal.
c) Compute the
commutators
[
σ
x
,σ
y
],[
σ
y
,σ
z
], and [
σ
z
,σ
x
]
d) Use the eigenstates of
σ
x
as a basis, and rewrite
σ
x
,
σ
y
, and
σ
z
in this new basis.
(Hint: Simply apply the similarity transformation generated by diagonalizing
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Unformatted text preview: σ x to σ y and σ z .) Can you see a connection to a rotation about the yaxis? 2. Boas, Chapter 3, Section 6, Prob. 20 3. Boas, Chapter 3, Section 7, Prob. 26 4. Boas, Chapter 3, Section 7, Prob. 27 5. Boas, Chapter 3, Section 8, Prob. 4 6. Boas, Chapter 3, Section 8, Prob. 25 7. Boas, Chapter 3, Section 11, Prob. 16 8. Boas, Chapter 3, Section 12, Prob. 16 1...
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This note was uploaded on 07/30/2011 for the course PHZ 3113 taught by Professor Staff during the Spring '03 term at University of Central Florida.
 Spring '03
 Staff

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