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

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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 ⋅ + = + + + = +...
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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.

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