Abstract |
| In this article, a method is presented for transforming the singular Lippmann-Schwinger integral equation to a matrix algebraic equation. This method of computing the matrix elements of the reaction and transition operators is used on the real axis and on the complex plane, respectively. By specifying the elements value of the reaction and transition matrix on the energy-shell, both phase shifts and the differential scattering amplitudes and the differential cross- sections are computable. The presented method for the Gaussian quadratures is suitably based on the Legendre, Laguerre, Hermite, Jacobi, Chebyshev, and shifted Chebyshev polynomials, and the selection of the nodal points and the weight functions is dependent on the physics of the problem considered and the user's view. |
Keywords and phrases
transition matrix, reaction matrix, Lippmann-Schwinger equation, Gaussian quadratures, numerical analysis, quantum scattering theory.
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