| /* 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__ */ |
