Fourier Grid Hamiltonian (FGH) 1D Program

FGH Introduction

The FGH1D program calculates the eigenvalues (energy levels) and eigenvectors (wavefunctions) for an arbitrary one-dimensional potential. The program can generate potentials of a few fixed forms: Morse, polynomial in x2 - for double wells, cos(nx) - for internal rotations. The program can read in potentials from a file or from the clipboard in the form of x,y pairs. It can interpolate these potentials with a spline fit. FGH1D solves the Shrödinger equation variationally using the clever Fourier Grid Hamiltonian method as developed by C. C. Marston and G. G. Balint-Kurti (J. Chem. Phys. 91(6), 3571, 1989) (see also Balint-Kurti's home page). Basically it is similar to other discrete variable representation (DVR) methods except that it uses a basis set of delta functions rather than gaussians. This particular implementation requires an even number of grid points (basis functions). For most potentials the first n/3 eigenvalues are reasonable when n well-distributed grid points are used. The accuracy increases with increasing number of grid points.