diff options
Diffstat (limited to 'gsl-1.9/specfunc/gsl_sf_coulomb.h')
| -rw-r--r-- | gsl-1.9/specfunc/gsl_sf_coulomb.h | 128 |
1 files changed, 128 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/gsl_sf_coulomb.h b/gsl-1.9/specfunc/gsl_sf_coulomb.h new file mode 100644 index 0000000..588bc91 --- /dev/null +++ b/gsl-1.9/specfunc/gsl_sf_coulomb.h @@ -0,0 +1,128 @@ +/* specfunc/gsl_sf_coulomb.h + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation; either version 2 of the License, or (at + * your option) any later version. + * + * This program is distributed in the hope that it will be useful, but + * WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + * General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. + */ + +/* Author: G. Jungman */ + +#ifndef __GSL_SF_COULOMB_H__ +#define __GSL_SF_COULOMB_H__ + +#include <gsl/gsl_mode.h> +#include <gsl/gsl_sf_result.h> + +#undef __BEGIN_DECLS +#undef __END_DECLS +#ifdef __cplusplus +# define __BEGIN_DECLS extern "C" { +# define __END_DECLS } +#else +# define __BEGIN_DECLS /* empty */ +# define __END_DECLS /* empty */ +#endif + +__BEGIN_DECLS + + +/* Normalized hydrogenic bound states, radial dependence. */ + +/* R_1 := 2Z sqrt(Z) exp(-Z r) + */ +int gsl_sf_hydrogenicR_1_e(const double Z, const double r, gsl_sf_result * result); +double gsl_sf_hydrogenicR_1(const double Z, const double r); + +/* R_n := norm exp(-Z r/n) (2Z/n)^l Laguerre[n-l-1, 2l+1, 2Z/n r] + * + * normalization such that psi(n,l,r) = R_n Y_{lm} + */ +int gsl_sf_hydrogenicR_e(const int n, const int l, const double Z, const double r, gsl_sf_result * result); +double gsl_sf_hydrogenicR(const int n, const int l, const double Z, const double r); + + +/* Coulomb wave functions F_{lam_F}(eta,x), G_{lam_G}(eta,x) + * and their derivatives; lam_G := lam_F - k_lam_G + * + * lam_F, lam_G > -0.5 + * x > 0.0 + * + * Conventions of Abramowitz+Stegun. + * + * Because there can be a large dynamic range of values, + * overflows are handled gracefully. If an overflow occurs, + * GSL_EOVRFLW is signalled and exponent(s) are returned + * through exp_F, exp_G. These are such that + * + * F_L(eta,x) = fc[k_L] * exp(exp_F) + * G_L(eta,x) = gc[k_L] * exp(exp_G) + * F_L'(eta,x) = fcp[k_L] * exp(exp_F) + * G_L'(eta,x) = gcp[k_L] * exp(exp_G) + */ +int +gsl_sf_coulomb_wave_FG_e(const double eta, const double x, + const double lam_F, + const int k_lam_G, + gsl_sf_result * F, gsl_sf_result * Fp, + gsl_sf_result * G, gsl_sf_result * Gp, + double * exp_F, double * exp_G); + + +/* F_L(eta,x) as array */ +int gsl_sf_coulomb_wave_F_array( + double lam_min, int kmax, + double eta, double x, + double * fc_array, + double * F_exponent + ); + +/* F_L(eta,x), G_L(eta,x) as arrays */ +int gsl_sf_coulomb_wave_FG_array(double lam_min, int kmax, + double eta, double x, + double * fc_array, double * gc_array, + double * F_exponent, + double * G_exponent + ); + +/* F_L(eta,x), G_L(eta,x), F'_L(eta,x), G'_L(eta,x) as arrays */ +int gsl_sf_coulomb_wave_FGp_array(double lam_min, int kmax, + double eta, double x, + double * fc_array, double * fcp_array, + double * gc_array, double * gcp_array, + double * F_exponent, + double * G_exponent + ); + +/* Coulomb wave function divided by the argument, + * F(eta, x)/x. This is the function which reduces to + * spherical Bessel functions in the limit eta->0. + */ +int gsl_sf_coulomb_wave_sphF_array(double lam_min, int kmax, + double eta, double x, + double * fc_array, + double * F_exponent + ); + + +/* Coulomb wave function normalization constant. + * [Abramowitz+Stegun 14.1.8, 14.1.9] + */ +int gsl_sf_coulomb_CL_e(double L, double eta, gsl_sf_result * result); +int gsl_sf_coulomb_CL_array(double Lmin, int kmax, double eta, double * cl); + + +__END_DECLS + +#endif /* __GSL_SF_COULOMB_H__ */ |