Unformatted text preview: . Also notice that for â†’ Îµ we have ) ( 2 ) ( ) ) ( ( 2 ) ( ) ) ( ( 2 ) ( 2 2 2 2 2 Î± h h h m dx x E x m dx x E x V m dx dx x d âˆ’ = âˆ’ âˆ’ = âˆ’ = âˆ« âˆ« âˆ« + âˆ’ + âˆ’ + âˆ’ Thus, ) ( 2 ) ( 2 ) ( ) ( 2 2 L R x L x R m m dx x d dx x d h h âˆ’ = âˆ’ = âˆ’ âˆ’ = + = which implies that D m A D 2 2 h âˆ’ = âˆ’ âˆ’ but A = D and hence 2 h m = . Thus there is only one allowed energy ( i.e. one bound state) given by 2 2 2 h m E âˆ’ = and h h /   ) ( x m e m x âˆ’ = , where I have normalized Ïˆ (x) so that < Ïˆ  Ïˆ > = 1. x V Î±Î´ (x)...
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 Spring '07
 FIELDS
 mechanics, Quantum Field Theory, dx, bound states, bound state, De âˆ’Îºx

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