A new multi-purpose software package for Schrödinger and Sturm-Liouville computations

Abstract In this paper we describe a new software package which is currently being developed at the Royal Military College of Science. It aims to provide facilities for basic computations related to the Schrodinger equation and second-order linear Sturm-Liouville problems. The new routines are less problem-specific than most software currently available, while offering significant advantages in speed over existing library software, and significant advantages in accuracy over other general-purpose methods such as finite-difference methods.

[1]  L. Ixaru,et al.  Choosing step sizes for perturbative methods of solving the Schrödinger equation , 1980 .

[2]  Frank de Hoog,et al.  Uniform estimation of the eigenvalues of Sturm–Liouville problems , 1980, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[3]  N. Fröman,et al.  Phase‐integral calculation of quantal matrix elements without the use of wavefunctions , 1977 .

[4]  Steven Pruess,et al.  Estimating the Eigenvalues of Sturm–Liouville Problems by Approximating the Differential Equation , 1973 .

[5]  N. Fröman,et al.  A direct method for modifying certain phase-integral approximations of arbitrary order , 1974 .

[6]  Roy G. Gordon,et al.  New Method for Constructing Wavefunctions for Bound States and Scattering , 1969 .

[7]  R. L. Roy,et al.  Bound → continuum intensities — A computer program for calculating absorption coefficients, emission intensities or (golden rule) predissociation rates , 1989 .

[8]  John D. Pryce,et al.  Error Control of Phase-Function Shooting Methods for Sturm-Liouville Problems , 1986 .

[9]  C. Jedrzejek,et al.  Phase-integral and numerical calculations of matrix elements and Franck-Condon factors for Morse oscillators , 1987 .

[10]  N. Fröman,et al.  On modifications of phase integral approximations of arbitrary order , 1974 .

[11]  N. Fröman.  Connection formulas for certain higher order phase-integral approximations , 1970 .

[12]  N. Fröman.  A simple formula for calculating quantal expectation values without the use of wave functions , 1974 .

[13]  L. Ixaru.  The error analysis of the algebraic method for solving the Schrödinger equation , 1972 .

[14]  J. Tienari,et al.  Efficient computation of the Pru¨fer phase function for determining eigenvalues of Sturm-Liouville systems , 1986 .