This preview shows page 1. Sign up to view the full content.
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> = j'j 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> = (m1) ((J ) op jm>) and hence (J ) op jm> = c jm1> . The operators (J ) op shifts the state jm> to a new state jm1> 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!...
View Full
Document
 Spring '07
 FIELDS
 mechanics, Angular Momentum, Momentum

Click to edit the document details