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: ----------- 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. |