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Manuscript Title: Two computer programs for solving the Schrodinger equation for bound state eigenvalues and eigenfunctions using the Fourier Grid Hamiltonian method.
Authors: G.G. Balint-Kurti, C.L. Ward, C.C. Marston
Program title: FGHFFT
Catalogue identifier: ACBQ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 67(1991)285
Programming language: Fortran.
Computer: IBM 3090.
Operating system: CMS.
RAM: 1000K words
Word size: 64
Keywords: General purpose, Differential equation, Bound states, Eigenvalues, Eigenfunctions, Schrodinger equation.
Classification: 4.3.

Nature of problem:
The program solves the one dimensional Schrodinger equation numerically to any desired degree of accuracy. The solutions are needed in molecular spectroscopy, molecular scattering theory and photodissoci- ation theory. They may also be used as a component of a more extensive code for solving the Schrodinger equation in more than one dimension.

Solution method:
A regular grid of points is defined which spans the region of interest. A hamiltonian matrix is then calculated using the discrete Fast Fourier Transform method to compute the kinetic energy part of the operator. The potential energy part of the hamiltonian matrix is diagonal, requiring only the evaluation of the potential on the grid points (V(xi)). The eigenvalues and eigenvectors of this matrix are then found. The eigenvalues which lie below the asymptotic value of the potential (V(x=infinity)) are the bound state energies and the corresponding eigenvectors are the eigenfunctions evaluated at the grid points. The program FGHFFT differs from FGHEVEN only in the method used to evaluate the kinetic energy part of the hamiltonian matrix. This should make the program more efficient, although less transparent, for larger numbers of grid points.

The Schrodinger equation must be in one dimension only and the coordinate involved must correspond to a radial or length type coordinate. The potential must possess a minimum and at short distances it must be very large and positive (repulsive). The number of grid points must be a power of 2 due to the nature of the Fast Fourier Transform subroutine used.

Running time:
10 seconds.