Chapter4_18

Chapter4_18 - PHY4604 R. D. Field Department of Physics...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PHY4604 R. D. Field Department of Physics Chapter4_18.doc University of Florida The Pauli Matrices Consider the three Pauli matrices = 1 1 x σ − = i i y σ − = 1 1 z σ These matricides have σ ↑ i = σ i det( σ i ) = -1 Tr( σ i ) = 0 [ σ i , σ j ] = 2i ε ijk σ k { σ i , σ j } = 2 δ ij . They are hermitian, traceless, and they anti-commute ( σ x 2 = σ y 2 = σ z 2 = 1). Define − + = ± = ± 1 1 1 1 ) ( 2 1 2 1 2 1 y x i σ σ σ hence = + 1 σ = − 1 σ also = + 1 ) ( 2 1 z I σ = − 1 ) ( 2 1 z I σ where = 1 1 I . Arbitrary 2×2 Matrix: Any 2×2 matrix can be written as σ σ σ σ r r ⋅ + = + + + = +...
View Full Document

This note was uploaded on 05/29/2011 for the course PHY 4064 taught by Professor Fields during the Spring '07 term at University of Florida.

Ask a homework question - tutors are online