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Manuscript Title: Accurate numerical solution of the Schrodinger and Dirac wave equations for central fields.
Authors: F. Salvat, R. Mayol
Program title: RADWEQ
Catalogue identifier: ABTR_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 62(1991)65
Programming language: Fortran.
Computer: IBM 3090/170S.
Operating system: VM/HPO REL.5, VMS REL.4.7, MS-DOS 3.3.
RAM: 160K words
Word size: 8
Keywords: General purpose, Differential equation, Schrodinger equation, Dirac equation, Central fields, Bound states, Free states, Eigenvalues, Phase shifts.
Classification: 4.3.

Nature of problem:
This subroutine package provides numerical solutions of the Schrodinger and Dirac equations for central fields such that V(r)->0 when r-> infinity and rV(r) is finite for r=0. Radial wave functions, eigenvalues for bound states and phase shifts for free states are evaluated with a prescribed accuracy. Results are delivered to the main program after calling a single subroutine.

Solution method:
The function V(r)=rV(r) is approximated by a cubic spline that interpolates the V(r) values of a table introduced by the user. The radial wave equations are solved by using the power series method due to Buhring. The magnitude of the numerical uncertainity of the results is controlled through the input parameter epsilon. Typically, a value of epsilon=10**-n leads to results with (n-1)-decimal-place accuracy. This is only an order-of-magnitude estimate, a more realistic indication of the magnitude of the global errors may be determined by inspection of the results obtained with different epsilon values.

Restrictions:
Bound states with multiple zeros between two consecutive grid points cannot be solved without increasing the density of the input grid. In such a case, the program asks for a denser grid.

Unusual features:
The present algorithms offer the possibility of selecting the accuracy of the numerical solution. When using optimum accuracy (i.e. epsilon~ 10**-15 with double precision arithmetic) truncation errors, inherent to most numerical integration methods, are effectively eliminated. In this case, the only remaining uncertainties are due to unavoidable round-off errors and to the distortion of the potential introduced by the interpolating spline (which may be reduced by simply using a denser input grid).

Running time:
For a given problem, the running time increases when increasing the desired accuracy (decreasing epsilon) or the energy. The calculation of the ground state of the hydrogen atom with epsilon= 10**-10 takes about 0.25 seconds on the IBM 3090/170, 10 seconds on the VAX 2000 and 40 seconds on the IBM/PS2.