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Assignment #7
PHYS446
due in class on 21 November 2008
1. Prove Schwarz Inequality:
∣⟨
a
∣
b
⟩∣ ∣
a
∣ ∣
b
∣
To do this, consider the axiom
⟨
c
∣
c
⟩
0 , applied to
∣
c
⟩
=
∣
a
⟩
−
⟨
b
∣
a
⟩
∣
b
∣
2
∣
b
⟩
2. (Griffiths, Problem 3.27) An operator
A
, representing observable
A
, has two normalized
eigenstates
1
and
2
, with eigenvalues
a
1
and
a
2
, respectively. Operator
B
,
representing observable
B
, has two normalized eigenstates
1
and
2
, with eigenvalues
b
1
and
b
2
. The eigenstates are related by
1
=
3
1
4
2
/
5,
2
=
4
1
−
3
2
/
5
(a) Observable
A
is measured, and the value
a
1
is obtained. What is the state of the system
(immediately) after this measurement?
(b) If
B
is now measured, what are the possible results, and what are their probabilities?
(c) Right after the measurement of
B
,
A
is measured again. What is the total probability of
getting back a value
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 Fall '08
 Vachon
 mechanics

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