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Lecture 32:
Symmetry III:
Discrete symmetries
PHY851 Quantum Mechanics I
Fall, 2008
M.G. Moore
Quiz #11
•
Compute:
–
And
–
What is:
?
•
Hint:
use
to turn it into a product
of things you already know
)
(
)
(
†
d
XT
d
T
X
=
!
)
(
)
(
†
d
PT
d
T
P
=
!
)
(
)
(
†
2
d
T
X
d
T
T
+
(
d
)
T
(
d
)
=
1
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View Full Document Discrete Symmetry
•
A discrete symmetry is a transformation
which is parameterized by a discrete index
•
The simplest discrete symmetry is Parity
–
Defined as mirror reversal about a plane
•
Since the parity transformation switches
the ‘handedness’ of a coordinate system, it
cannot be represented as any combination of
rotations
Parity Operator
•
Let us define the parity operator via:
–
Parity operator is Hermitian:
–
Parity operator is Unitary
–
In fact it is its own inverse!
•
Parity acting to the left:
1
2
=
!
!
"
#
=
#
+
=
#
$
=
#
"
x
x
x
x
x
x
x
x
)
(
%
!
=
!
†
x
x
x
=
!
"
=
"
"
†
1
†
!
"
=
"
x
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This note was uploaded on 10/25/2010 for the course PHYSICS PHYS 851 taught by Professor Michaelmoore during the Fall '08 term at Michigan State University.
 Fall '08
 MichaelMoore
 mechanics

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