Mathematical Methods in Quantum and Statistical Mechanics.

The J-matrix method, was extended to treat the script l to the th power partial wave kinetic energy and Coulomb Hamiltonians within the context of square integrable, Laguerre (Slater), and oscillator (Gaussian) basis sets. The determination of the expansion coefficients of the continuum eigenfunctions in terms of the L sub 2 basis set is shown to be equivalent to the solution of a linear second-order differential equation with appropriate boundary conditions, and complete solutions are presented. Physical scattering problems were approximated by a well-defined model which was then solved exactly. The appropriate formalism for treating many channel problems where target states of differing angular momentum were coupled was spelled out in detail. The method involved the evaluation of only L sub 2 matrix elements and finite matrix operations, yielding elastic and inelastic scattering information over a continuous range of energies.