Lect32_Discrete_Symmetry - Quiz #11 Compute: And X ! = T (d...

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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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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 ‘handed-ness’ of a coordinate system, it cannot be represented as any combination of rotations
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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.

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Lect32_Discrete_Symmetry - Quiz #11 Compute: And X ! = T (d...

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