Dirac_14 - op S H L H S L H J H r r r r r and hence the total angular momentum is conserved Furthermore k ijk j i S i S S ε h = and = I I S 4 3 2

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PHY4604 R. D. Field Department of Physics Dirac_14.doc University of Florida Total Angular Momentum J We see that ) ( ] , [ op op op p c i L H r r h r × = α and ) ( ] , [ op op op p c i S H r r h r × + = and hence neither the orbital angular momentum L r or the spin angular momentum S r is conserved. Total Angular Momentum: The total angular momentum operator is given by op op op S L J r r r + = where op op op p r L r r r × = and = σ r r h r 0 0 2 op S . We see that 0 ] , [ ] , [ ] , [ ] , [ = + = + = op op op op op op op op
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Unformatted text preview: op S H L H S L H J H r r r r r and hence the total angular momentum is conserved! Furthermore, k ijk j i S i S S ε h = ] , [ and = I I S 4 3 2 2 h and the eigenvalues of z S are h 2 1 ± . Hence, the Dirac equation describes relativistic particles and antiparticles that carry intrinsic spin ½ !...
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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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