Dear GSL folks,
I ran into a problem with your routines for calculating F_L and G_L, the
partial-wave solutions for the Coulomb problem. The functions are
discontinuous,
as the functions flip signs for values of x~3.2 and x~5.8 in the
example below.
I'm working with GSL 1.7
Thanks for everything, - Scott Pratt
#include <cstdio>
#include <cmath>
#include <gsl/gsl_sf.h>
int main(){
int L=2,dummy;
double x,eta=0.1;
double expF,expG;
double *fc,*gc;
fc=new double[L+1];
gc=new double[L+1];
printf("eta=%g\n",eta);
printf("x ____ F(L=0) G(L=0) ___ F(L=1) G(L=1) ___ F(L=2) G(L=2)
___\n");
for(x=0.1;x<7;x+=0.05){
dummy=gsl_sf_coulomb_wave_FG_array(0,L,eta,x,fc,gc,&expF,&expG);
expF=exp(expF);
expG=exp(expG);
printf("%4.2f %7.3f %7.3f %7.3f %7.3f %7.3f %7.3f\n",
x,fc[0]*expF,gc[0]*expG,fc[1]*expF,gc[1]*expG,fc[2]*expF,gc[2]
*expG);
}
delete [] fc;
delete [] gc;
return 0;
}
____________________ OUTPUT_______________________
x ____ F(L=0) G(L=0) ___ F(L=1) G(L=1) ___ F(L=2) G(L=2) ___
0.10 0.098 1.007 0.003 10.199 0.000 305.112
0.15 0.147 1.000 0.007 6.838 0.000 135.856
0.20 0.196 0.990 0.013 5.169 0.001 76.625
0.25 0.244 0.979 0.020 4.178 0.001 49.215
0.30 0.292 0.965 0.029 3.524 0.002 34.329
0.35 0.339 0.949 0.040 3.064 0.003 25.356
0.40 0.385 0.931 0.052 2.723 0.004 19.535
0.45 0.430 0.910 0.065 2.463 0.006 15.547
0.50 0.474 0.887 0.080 2.258 0.008 12.696
0.55 0.517 0.863 0.097 2.094 0.011 10.589
0.60 0.559 0.836 0.114 1.959 0.014 8.988
0.65 0.600 0.807 0.133 1.847 0.018 7.745
0.70 0.639 0.776 0.154 1.752 0.022 6.760
0.75 0.676 0.743 0.175 1.671 0.027 5.967
0.80 0.712 0.709 0.198 1.601 0.032 5.320
0.85 0.746 0.673 0.221 1.540 0.038 4.785
0.90 0.778 0.635 0.246 1.485 0.045 4.338
0.95 0.809 0.595 0.272 1.436 0.053 3.962
1.00 0.837 0.554 0.298 1.392 0.061 3.642
1.05 0.863 0.512 0.325 1.351 0.070 3.368
1.10 0.888 0.469 0.353 1.313 0.080 3.132
1.15 0.910 0.424 0.381 1.277 0.091 2.926
1.20 0.930 0.378 0.410 1.243 0.103 2.747
1.25 0.947 0.332 0.440 1.210 0.115 2.590
1.30 0.962 0.284 0.469 1.178 0.128 2.452
1.35 0.975 0.236 0.499 1.146 0.142 2.329
1.40 0.985 0.187 0.529 1.115 0.157 2.219
1.45 0.993 0.138 0.560 1.084 0.173 2.121
1.50 0.999 0.088 0.590 1.053 0.189 2.034
1.55 1.002 0.039 0.620 1.022 0.206 1.954
1.60 1.003 -0.011 0.649 0.990 0.224 1.882
1.65 1.001 -0.061 0.679 0.958 0.243 1.817
1.70 0.997 -0.111 0.707 0.925 0.263 1.757
1.75 0.990 -0.160 0.736 0.891 0.283 1.701
1.80 0.980 -0.209 0.764 0.857 0.304 1.650
1.85 0.969 -0.258 0.791 0.822 0.325 1.603
1.90 0.955 -0.305 0.817 0.786 0.347 1.558
1.95 0.938 -0.352 0.842 0.749 0.370 1.516
2.00 0.920 -0.399 0.867 0.712 0.393 1.477
2.05 0.899 -0.444 0.890 0.673 0.417 1.439
2.10 0.875 -0.488 0.912 0.634 0.442 1.403
2.15 0.850 -0.531 0.933 0.593 0.466 1.368
2.20 0.822 -0.573 0.953 0.552 0.491 1.334
2.25 0.793 -0.613 0.971 0.511 0.517 1.301
2.30 0.761 -0.651 0.988 0.468 0.542 1.269
2.35 0.728 -0.689 1.003 0.425 0.568 1.237
2.40 0.693 -0.724 1.017 0.381 0.594 1.205
2.45 0.656 -0.757 1.029 0.336 0.620 1.174
2.50 0.617 -0.789 1.040 0.291 0.646 1.143
2.55 0.577 -0.819 1.048 0.245 0.672 1.111
2.60 0.536 -0.847 1.055 0.199 0.698 1.079
2.65 0.493 -0.872 1.060 0.153 0.723 1.047
2.70 0.449 -0.896 1.063 0.106 0.749 1.015
2.75 0.404 -0.917 1.065 0.059 0.774 0.982
2.80 0.357 -0.936 1.064 0.012 0.798 0.949
2.85 0.310 -0.952 1.061 -0.035 0.823 0.915
2.90 0.263 -0.967 1.057 -0.082 0.846 0.881
2.95 0.214 -0.978 1.050 -0.129 0.870 0.846
3.00 0.165 -0.988 1.041 -0.175 0.892 0.810
3.05 0.116 -0.995 1.031 -0.221 0.914 0.774
3.10 0.066 -0.999 1.018 -0.267 0.935 0.737
3.15 0.016 -1.001 1.004 -0.312 0.955 0.699
3.20 0.034 1.001 -0.987 0.357 -0.974 -0.661
3.25 0.084 0.998 -0.968 0.401 -0.992 -0.622
3.30 0.133 0.993 -0.948 0.444 -1.009 -0.582
3.35 0.183 0.985 -0.925 0.486 -1.025 -0.542
3.40 0.232 0.974 -0.901 0.528 -1.040 -0.501
3.45 0.280 0.962 -0.875 0.568 -1.054 -0.459
3.50 0.327 0.946 -0.847 0.607 -1.066 -0.417
3.55 0.374 0.929 -0.817 0.644 -1.077 -0.375
3.60 0.420 0.909 -0.786 0.681 -1.086 -0.332
3.65 0.465 0.887 -0.752 0.716 -1.094 -0.288
3.70 0.508 0.863 -0.718 0.749 -1.101 -0.244
3.75 0.551 0.836 -0.682 0.781 -1.106 -0.200
3.80 0.592 0.808 -0.644 0.811 -1.110 -0.155
3.85 0.631 0.777 -0.605 0.839 -1.112 -0.111
3.90 0.669 0.745 -0.564 0.866 -1.112 -0.066
3.95 0.705 0.711 -0.523 0.891 -1.110 -0.021
4.00 0.740 0.674 -0.480 0.914 -1.107 0.025
4.05 0.773 0.637 -0.436 0.935 -1.103 0.070
4.10 0.803 0.597 -0.392 0.953 -1.096 0.114
4.15 0.832 0.557 -0.346 0.970 -1.088 0.159
4.20 0.859 0.514 -0.300 0.985 -1.078 0.204
4.25 0.883 0.471 -0.253 0.997 -1.066 0.248
4.30 0.906 0.426 -0.205 1.007 -1.052 0.292
4.35 0.926 0.381 -0.157 1.015 -1.037 0.335
4.40 0.944 0.334 -0.109 1.021 -1.020 0.378
4.45 0.959 0.286 -0.060 1.024 -1.001 0.420
4.50 0.972 0.238 -0.012 1.026 -0.980 0.461
4.55 0.983 0.189 0.037 1.024 -0.958 0.501
4.60 0.991 0.140 0.086 1.021 -0.934 0.541
4.65 0.997 0.091 0.134 1.015 -0.908 0.580
4.70 1.000 0.041 0.182 1.007 -0.881 0.617
4.75 1.001 -0.009 0.230 0.997 -0.852 0.654
4.80 0.999 -0.059 0.277 0.984 -0.822 0.689
4.85 0.995 -0.109 0.324 0.969 -0.790 0.723
4.90 0.988 -0.158 0.370 0.952 -0.756 0.756
4.95 0.979 -0.208 0.415 0.933 -0.722 0.787
5.00 0.968 -0.256 0.459 0.912 -0.685 0.817
5.05 0.954 -0.304 0.502 0.888 -0.648 0.845
5.10 0.937 -0.351 0.544 0.863 -0.609 0.872
5.15 0.919 -0.398 0.584 0.836 -0.569 0.897
5.20 0.898 -0.443 0.624 0.806 -0.528 0.920
5.25 0.874 -0.487 0.662 0.775 -0.486 0.942
5.30 0.849 -0.530 0.698 0.742 -0.444 0.961
5.35 0.822 -0.572 0.733 0.707 -0.400 0.979
5.40 0.792 -0.612 0.766 0.671 -0.355 0.995
5.45 0.760 -0.651 0.797 0.633 -0.310 1.009
5.50 0.727 -0.688 0.826 0.594 -0.264 1.021
5.55 0.692 -0.723 0.854 0.553 -0.218 1.030
5.60 0.655 -0.757 0.879 0.511 -0.171 1.038
5.65 0.616 -0.789 0.903 0.468 -0.123 1.044
5.70 0.576 -0.818 0.924 0.423 -0.076 1.048
5.75 0.535 -0.846 0.943 0.378 -0.028 1.049
5.80 -0.492 0.872 -0.960 -0.332 -0.019 -1.048
5.85 -0.448 0.895 -0.975 -0.285 -0.067 -1.045
5.90 -0.402 0.916 -0.987 -0.237 -0.114 -1.041
5.95 -0.356 0.935 -0.997 -0.189 -0.162 -1.033
6.00 -0.309 0.952 -1.005 -0.140 -0.209 -1.024
6.05 -0.261 0.966 -1.010 -0.091 -0.255 -1.013
6.10 -0.213 0.978 -1.013 -0.042 -0.301 -0.999
6.15 -0.164 0.987 -1.014 0.007 -0.346 -0.984
6.20 -0.114 0.994 -1.012 0.057 -0.391 -0.966
6.25 -0.064 0.999 -1.008 0.106 -0.435 -0.946
6.30 -0.014 1.001 -1.001 0.155 -0.478 -0.925
6.35 -0.036 -1.000 0.993 -0.203 0.519 0.901
6.40 -0.085 -0.997 0.981 -0.251 0.560 0.876
6.45 -0.135 -0.992 0.968 -0.299 0.600 0.848
6.50 -0.184 -0.984 0.952 -0.345 0.638 0.819
6.55 -0.233 -0.973 0.934 -0.391 0.675 0.788
6.60 -0.282 -0.960 0.913 -0.436 0.710 0.755
6.65 -0.329 -0.945 0.891 -0.480 0.744 0.721
6.70 -0.376 -0.927 0.866 -0.523 0.777 0.685
6.75 -0.422 -0.908 0.839 -0.565 0.807 0.648
6.80 -0.466 -0.885 0.811 -0.605 0.836 0.609
6.85 -0.510 -0.861 0.780 -0.644 0.863 0.569
6.90 -0.552 -0.834 0.748 -0.681 0.889 0.528
6.95 -0.593 -0.806 0.713 -0.717 0.912 0.486
7.00 -0.633 -0.775 0.677 -0.750 0.933 0.442
% ____________________________________________________________________
% Scott Pratt [EMAIL PROTECTED]
% Dept. of Physics and Astronomy http://www.pa.msu.edu/~pratts
% 4208A BioMedical Physical Sci. Bldg.
% Michigan State University (517) 355-9200, ext. 2016
% East Lansing, MI 48824-2320 fax: (517) 353-4500
% ____________________________________________________________________
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