The Kohn Hulthen Variational Procedure for the Scattering Operator And the React

Harry Elecks Moses

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U) 0^ (x|x ) ' -j^ ■ F—, x-x 4 t -I ^-i lit I |x-x I (5. 5) of(, |x', . -^=_lj^.
/r ^\ «B/ I '\ 1 COSlkllx-X I 2 In (5. Ii)-(5. 6), E - |k| • Again we shall express our results in terms of the momentum representation. The appropriate eigenfvinctions in terms of this repre- sentation are /r- ^\ « / 1, V 1 i(K»x) (5. 7) Vxlk) - -—JJ2^ '—' (2ii)- (5. 8) Y (x|k) - --±^e^(^^^ - ^ r . . V(x )T (X |k)dx, (2n) J |x-x I V5IS) • -^'''^-^'-fe ^°-|Sl l W lv(x')Vx'|K)dx'.
- lU - The function can be expres...sed in terms of the amplitude of the spherical wave obtained hj letting |x| ->oo in T_(x|k): 1 1 If 'T (5. 10) lim T (x|k) - — ±, ^e^^i^ |xl-^oo - (27T)^/^ ^ e^'~'l^l . • -1/2 > ' -V^ [ ^[|t^| (sinSsin© ) ^^\^ .
The variables 6, ^ are now the degeneracy variables previously collectively de- noted by a. In fact in (3. 6) we have (5. 10a) |k| «= V^ ; G is the angle which k makes with the z-axis and

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