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

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