[Help-gsl] Usage of gsl_sf_coulomb_wave_FG_e

[Ivan Liu]

Hi,
I'm trying to test the function gsl_sf_coulomb_wave_FG_e and I want to
reproduce the result from gsl_sf_hydrogenicR using this function, but
I can't:

Command:

$ c++ -o run run.cc -lm -lgsl -lgslcblas
$ run
1.1     0.349982        0.183584
1.2     0.243029        0.155227
1.3     0.136783        0.1292
1.4     0.032991        0.105342
1.5     -0.0669617      0.0835034
1.6     -0.161994       0.0635447
1.7     -0.251279       0.0453342
1.8     -0.334207       0.0287488
1.9     -0.41035        0.0136734
2       -0.479431       -1.15521e-16

The program is below:


// calculate Rydberg wavefunction with given quantum defect.
#include <iostream>
#include <cmath>
#include <fstream>
#include <gsl/gsl_sf_coulomb.h>

using namespace std;

int main(void)
{
  double eta,x,L;
  int k=0;
  gsl_sf_result F,Fp,G,Gp,C_L;
  double exp_F,exp_G;
  double F_L,G_L;

  double kk,KE;
  double z1=1.0;
  double z2=-1.0;
  double wavefunc;

  int n=2;
  double r = 1.0;

  int imax = 10;
  double dr = 0.1;


  for( int i=0; i < 10 ; i++){
    r += dr;

    KE = -1.0/(2.0*n*n)+1.0/r;    //kinetic enegry
    kk = sqrt( 2.0*KE );             //impulse
    eta = z1*z2/kk;                   //conversion of variables
    x = kk*r;                            //conversion of variables

    int status1 = gsl_sf_coulomb_wave_FG_e (eta, x, L, k, &F, &Fp, &G,
&Gp, &exp_F, &exp_G);

    int status2 = gsl_sf_coulomb_CL_e (L, eta, &C_L);

    F_L = F.val * exp(exp_F);
    G_L = G.val * exp(exp_G);

    wavefunc = C_L.val*F_L;

    double R_nl = gsl_sf_hydrogenicR ( n, (int)trunc(L), 1.0, r);

    cout << r << '\t' << wavefunc << '\t' << R_nl << endl;

  }//i-loop

  return 0;
}