Abstract
The Fourier-grid (FG) method is a recent L2 variational treatment of the quantum mechanical eigenvalue problem that does not require the use of a set of basis functions: it is rather a discrete variable representation approach. The author restates the FG philosophy in more general terms, examine and compare this method with other approaches to the eigenvalue problem, and begin the development of an FG R-matrix method for scattering. The philosophy of the FG method is to use the simplest representation for each of the kinetic and potential energy operators of the Hamiltonian, and use a generalized Fourier transform to put the matrix elements of one of the above operators in the same representation as the other, so the Hamiltonian has a single representation. Thus, the Hamiltonian is represented at discrete points in either configuration or its reciprocal space.
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