Extraction of Scattering Information from Fredholm Determinants Calculated in anL2Basis: A Chebyschev Discretization of the Continuum

Abstract

Using the "equivalent-quadrature" relationship between diagonalization of the $s$-wave kinetic energy $H^0$ in a Laguerre-type basis and Chebyschev quadrature of the second kind, a procedure is given by which potential-scattering phase shifts may be constructed from approximation to the Fredholm determinant constructed using only square-integrable ($L^2$) functions. For the problem of electron-hydrogen scattering in the static approximation, highly accurate phase shifts are obtained over a continuous range of energies from a single major computational step.