The Formulation of the Kohn Hulthen Variational Principle in Terms of the Scatte

Cover The Formulation of the Kohn Hulthen Variational Principle in Terms of the Scatte
The Formulation of the Kohn Hulthen Variational Principle in Terms of the Scatte
Harry E Moses
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Hence ACJ ) is an Insensitive functional of T - 6 - in the vicinity of s' . = T and we can write (27) M?^) - A(T^).
where J approximates T . It will also "be shown that (28) I(T^) = and that hence relation (27) can he written eT^(?, P«|?. P) = 1(?^)*€ -IT (F. P'If. P) = A(7_j_) or^ eqtii\ralently, (29) T_(F. P«|F, P) =iA(7^).
Relation (29) is the form of the Kohn-Holthen principle in terms of the scattering operator fomelism. We use trial f-unctions J in the right-hand side of (29) to ohtaln p
...more accurate expression for T^(T, P '|F, P).
It should he noted that in evaltiating the expression (25) for l(^_j^) one must take care not to interchange the limit and the integration processes prematurely. If one takes the limit hefore carrying out at least pert of the integration, the integrand is not defined hecause one has the product of two symholic fimctions ▼. V which have the same arguments in terms of the varia- hles S and I*. Products of symholic functions having the same argument ere generally not defined; however if the symholic functions have different argu- ments their products can he defined.


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