An Evaluation of Approximation Methods for Three Body Scattering Problems

Cover An Evaluation of Approximation Methods for Three Body Scattering Problems
An Evaluation of Approximation Methods for Three Body Scattering Problems
Solomon L Schwebel
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The procedure for the determination of these coefficients is exactly the same as that given in section (2. 2. 2). The result of the calculation yields V 2 2 (3. 2. 11) G(K^K2) = (K^K2|k^kp/(K^+K^-E), G(K^) = (K^2|k^k^)y (4-K^); ^ = B^+E G(X2) = (iKglk^kpy (4-Kj)i G(12) = -(I2|k^kp7 (K^+B^).
Froai (3. 2. 10) and (3. 2. 11) the Green's f\inction becomes (3. 2. 12) rf. . .. Vn /' ^^2'M4>^^^^2V2 "^l'^2> GO^k^jk'ky =J ^-- ■/ ■/ - 61 - (K^2llc^Jcp*dK^(K^2lk^k2) ilK^\)c*k^)*dX2 (lK2lk^k2) (I2lk^kp*(l2
...|k^k2) The identities (3. 2. ?) coupled with equation (3. 2. 12) yield G(k^k2;k_«kp = G(k2k^;k^k^). (3. 2. 13) Prom the orthogonality and clostire relations we see that the complex conj-ugates of the eigenfunctions also form a complete set. Thios the Green's function of equation (3, 2. 2) could be obtained as pn expansion in terms of the complex conjugates of the eigenfunctions. Therefore it follows from (3. 2. 12) that G(k^k2;k|k|) = G(k^k|;k^k2). (3. 2. 1^) In terms of the Green's fionction, the solution of equation (3.

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