Regularization in the J-matrix method of scattering revisited

We present an alternative, but equivalent, approach to the regularization of the reference problem in the J-matrix method of scattering. After identifying the regular solution of the reference wave equation with the “sine-like” solution in the J-matrix approach we proceed by direct integration   to find the expansion coefficients in an L²$L^2$ basis set that ensures a tridiagonal representation of the reference Hamiltonian. A differential equation in the energy is then deduced for these coefficients. The second independent solution of this equation, called the “cosine-like” solution, is derived by requiring it to pertain to the L²$L^2$ space. These requirements lead to solutions that are exactly identical to those obtained in the classical J-matrix approach. We find the present approach to be more direct and transparent than the classical differential approach of the J-matrix method.