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Manuscript Title: A program for the calculation of energy eigenvalues and eigenstates of a Schrodinger equation.
Authors: V. Fack, G. Vanden Berghe
Program title: SCHROD
Catalogue identifier: AADV_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 39(1986)187
Programming language: Fortran.
Computer: SIEMENS 7000 SERIES.
Operating system: BS2000.
RAM: 240K words
Word size: 32
Keywords: Nuclear physics, Schrodinger equation, Energy eigenvalues and Eigenfunctions, Finite difference Approach, Reduction of band width, Theoretical methods, General purpose, Differential equations.
Classification: 4.3, 17.16.

Nature of problem:
Calculation of the energy eigenvalues and eigenstates of the one dimensional Schrodinger equation d**2y(x) / dx**2 + (E - V(x))y(x) = 0 where E denotes the eigenvalue parameter and V(x) the potential.

Solution method:
A finite difference representation for d**2y(x) / dx**2 is introduced such that the Schrodinger equation is transformed into an algebraic eigenvalue problem. This problem can be reduced to the calculation of the eigenvalues and eigenvectors of a symmetric tridiagonal matrix, to which the NAG routine FO2BEF can be applied.

It is assumed that the wavefunctions are restricted to obey the Dirichlet boundary condition y(x)=0 at some x-value R.

Running time:
The running time depends on the choice of the value R, on the number of terms in the finite difference representation for d**2y(x) / dx**2 and on the considered steplength h.