Unformatted text preview: Also note that (J + ) op (J) op = (J 2 ) op (J z ) op ((J z ) op1) and (J) op (J + ) op = (J 2 ) op (J z ) op ((J z ) op +1). Eigenkets of (J 2 ) op and (J z ) op : Define jm> to be an eigenket of (J 2 ) op and (J z ) op with eigenvalues given by (J 2 ) op jm> = j(j+1)jm> and (J z ) op jm> = mjm> with <j'm'jm> = δ j'j δ m'm . We see that (J 2 ) op ((J ± ) op jm>)= (J ± ) op (J 2 ) op jm> = j(j+1) ((J ± ) op jm>) (J z ) op ((J ± ) op jm>)=( (J ± ) op (J z ) op ±(J z ) op )jm> = (m±1) ((J ± ) op jm>) and hence (J ± ) op jm> = c ± jm±1> . The operators (J ± ) op shifts the state jm> to a new state jm±1> with the same j value but with m shifted by ±1 . Note that at this point we do not know anything about j and m except that they are real numbers ( we are not assuming that they are integers ). Orthonormal set of states!...
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 Spring '07
 Field
 Physics, Angular Momentum, Momentum, Yi, op

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