SOME USEFUL DISCRETE VARIABLE REPRESENTATIONS FOR PROBLEMS IN TIME-DEPENDENT AND TIME-INDEPENDENT QUANTUM-MECHANICS

We develop a simple, yet powerful approach to constructing discrete variable representations for the solution of quantum mechanical problems by focusing on properties of the underlying basis set. Two examples, one involving fixed-node boundary conditions and the other periodic boundary conditions, are explicitly derived and applied to a problem in spherical polar coordinates with azimuthal symmetry. These two DVRs have equally spaced points and equal weights. © 1990.