Application of a Singular Wave-Function Operator in Scattering Theory
- 1 July 1961
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 2 (4), 482-490
- https://doi.org/10.1063/1.1703734
Abstract
A function which is defined in terms of the two‐body singular wave‐function matrix of Mo/ller acting on a plane‐wave state is calculated. In the paper by T. Pradhan, the function in question was obtained as the solution of a differential equation. Here, it is found that the function has a normalization which is different from the one assumed by Pradhan, and this behavior is attributed to the long‐range character of the Coulomb potential that is in the Mo/ller operator. An intermediate result of this paper agrees with the momentum‐space solution of the nonrelativistic Coulomb two‐body scattering problem which recently appeared in a paper published by S. Okubo and D. Feldman. As they show, the wave function must be renormalized to obtain the correct cross section, and this view is adopted in this paper. Consequently, the normalization assumed by Pradhan is reinstated. The Legendre expansion coefficients are calculated for the function, .
Keywords
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