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SCATTERH6 Library "JINRLIB" 
Author: O.Chuluunbaatar You are
Language: Fortran 
visitor here.
THE CALCULATIONS FOR A PHASE SHIFT AND WAVE FUNCTIONS
OF THE SCHROEDINGER EQUATIONS FOR A ONE-DIMENSIONAL
SCATTERING PROBLEM
The subroutine SCATTERH6 calculating a phase shift delta
and wave functions Psi of the Schroedinger equations
2
d 2
( ------ + k ) Psi(x) = V(x) * Psi(x)
2
dx
with boundary conditions:
Psi (x) -> 0 at x -> 0 or x -> -infinity,
Psi (x) -> sin(kx+delta) at x -> +infinity
on a uniform grid by the Bode quadrature formula [1] with a given
order of accuracy (from 2 up to 6) by the step h on a uniform grid.
Structure:
----------
Type: SUBROUTINE
User Entry Names: SCATTERH6
Internal Names: RSTEP XIVALUE1 PHI0
PHI1 GAUSSJ MUU
External References: POT,INITIAL -
user-supplied subprograms
Usage:
------
CALL SCATTERH6(DLAM1,PSI0,QQ,RMIN,RMAX,R,NN,IPOINT,EPS)
The input datas: QQ, RMIN, RMAX, R, NN, IPOINTS, EPS, where:
QQ is given momentum;
RMIN, RMAX are minimal and maximal values of independent
variable R on a finite interval [RMIN, RMAX];
R (I) are nodes of a grid;
NN is number of subintervals;
IPOINT is number of nodes of the Bode quadrature formula
(from 2 up to 6);
EPS is given accuracy of a calculation process.
Output datas: DLAM1, PSI0, where:
DLAM1 is value of a phase shift delta;
PSI0 (I) are values of a wave function Psi(R(I)).
FUNCTION POT (R) is compounded by the user for calculation of
the potential function V(x).
SUBROUTINE INITIAL (PSI0, DLAM0, QQ, R, IPOINT, N)
is compounded by the user for calculation of
asymptotic wave functions PSI0(1)...PSI0(IPOINT-1),
initial approximations: of wave functions
PSI0 (IPOINT)... PSI0 (N) and a phase shift DLAM0.
Method:
-------
Algorithm, on the basis of which the given subroutine was constructed
described in [2-4]. The accuracy of calculation -
up to O (h ^ (2 [(IPOINT+1) /2]).
Sources are submitted.
References:
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1. M. Abramowitz, I. Stegun, Handbook of mathematical
functions, National Bureau of Standarts, NY, 1964.
2. O. Chuluunbaatar, I.V. Puzynin, S.I. Vinitsky, Journal of
Computational Methods in Sciences and Engineering, 2002, v.2, p.37.
3. O. Chuluunbaatar, I.V. Puzynin, S.I. Vinitsky,
JINR preprint P11-01-61, Dubna 2001.
4. O. Chuluunbaatar, JINR abstract 11-2002-209, Dubna, 2002.
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