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Unformatted text preview: |S a > = S op | a > is an eigenstate of H op with eigenvalue a-s . The new eigenvalue is shifted by an amount -s ( i.e. lowering operator). Exponentiation: The operator op A e is defined by the power series expansion as follows: = ! 1 n n op n A A e op It is easy (but tedious) to show that L + + + + = ]]] , [ , [ , [ ]] , [ , [ ] , [ ! 3 1 ! 2 1 op op op op op op op op op op A op A B A A A B A A B A B e B e op op Hence, op A A op op e e 1 = . Also, op A op A B e B e op op = provided ] , [ = op op B A ....
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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.
- Spring '07