include/gsl/gsl_sf_coulomb.h

0001 /* specfunc/gsl_sf_coulomb.h
0002  *
0003  * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
0004  *
0005  * This program is free software; you can redistribute it and/or modify
0006  * it under the terms of the GNU General Public License as published by
0007  * the Free Software Foundation; either version 3 of the License, or (at
0008  * your option) any later version.
0009  *
0010  * This program is distributed in the hope that it will be useful, but
0011  * WITHOUT ANY WARRANTY; without even the implied warranty of
0012  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
0013  * General Public License for more details.
0014  *
0015  * You should have received a copy of the GNU General Public License
0016  * along with this program; if not, write to the Free Software
0017  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
0018  */
0019
0020 /* Author:  G. Jungman */
0021
0022 #ifndef __GSL_SF_COULOMB_H__
0023 #define __GSL_SF_COULOMB_H__
0024
0025 #include <gsl/gsl_mode.h>
0026 #include <gsl/gsl_sf_result.h>
0027
0028 #undef __BEGIN_DECLS
0029 #undef __END_DECLS
0030 #ifdef __cplusplus
0031 # define __BEGIN_DECLS extern "C" {
0032 # define __END_DECLS }
0033 #else
0034 # define __BEGIN_DECLS /* empty */
0035 # define __END_DECLS /* empty */
0036 #endif
0037
0038 __BEGIN_DECLS
0039
0040
0041 /* Normalized hydrogenic bound states, radial dependence. */
0042
0043 /* R_1 := 2Z sqrt(Z) exp(-Z r)
0044  */
0045 int gsl_sf_hydrogenicR_1_e(const double Z, const double r, gsl_sf_result * result);
0046 double gsl_sf_hydrogenicR_1(const double Z, const double r);
0047
0048 /* R_n := norm exp(-Z r/n) (2Z/n)^l Laguerre[n-l-1, 2l+1, 2Z/n r]
0049  *
0050  * normalization such that psi(n,l,r) = R_n Y_{lm}
0051  */
0052 int gsl_sf_hydrogenicR_e(const int n, const int l, const double Z, const double r, gsl_sf_result * result);
0053 double gsl_sf_hydrogenicR(const int n, const int l, const double Z, const double r);
0054
0055
0056 /* Coulomb wave functions F_{lam_F}(eta,x), G_{lam_G}(eta,x)
0057  * and their derivatives; lam_G := lam_F - k_lam_G
0058  *
0059  * lam_F, lam_G > -0.5
0060  * x > 0.0
0061  *
0062  * Conventions of Abramowitz+Stegun.
0063  *
0064  * Because there can be a large dynamic range of values,
0065  * overflows are handled gracefully. If an overflow occurs,
0066  * GSL_EOVRFLW is signalled and exponent(s) are returned
0067  * through exp_F, exp_G. These are such that
0068  *
0069  *   F_L(eta,x)  =  fc[k_L] * exp(exp_F)
0070  *   G_L(eta,x)  =  gc[k_L] * exp(exp_G)
0071  *   F_L'(eta,x) = fcp[k_L] * exp(exp_F)
0072  *   G_L'(eta,x) = gcp[k_L] * exp(exp_G)
0073  */
0074 int
0075 gsl_sf_coulomb_wave_FG_e(const double eta, const double x,
0076                             const double lam_F,
0077                             const int  k_lam_G,
0078                             gsl_sf_result * F, gsl_sf_result * Fp,
0079                             gsl_sf_result * G, gsl_sf_result * Gp,
0080                             double * exp_F, double * exp_G);
0081
0082
0083 /* F_L(eta,x) as array */
0084 int gsl_sf_coulomb_wave_F_array(
0085   double lam_min, int kmax,
0086   double eta, double x,
0087   double * fc_array,
0088   double * F_exponent
0089   );
0090
0091 /* F_L(eta,x), G_L(eta,x) as arrays */
0092 int gsl_sf_coulomb_wave_FG_array(double lam_min, int kmax,
0093                                 double eta, double x,
0094                                 double * fc_array, double * gc_array,
0095                                 double * F_exponent,
0096                                 double * G_exponent
0097                                 );
0098
0099 /* F_L(eta,x), G_L(eta,x), F'_L(eta,x), G'_L(eta,x) as arrays */
0100 int gsl_sf_coulomb_wave_FGp_array(double lam_min, int kmax,
0101                                 double eta, double x,
0102                                 double * fc_array, double * fcp_array,
0103                                 double * gc_array, double * gcp_array,
0104                                 double * F_exponent,
0105                                 double * G_exponent
0106                                 );
0107
0108 /* Coulomb wave function divided by the argument,
0109  * F(eta, x)/x. This is the function which reduces to
0110  * spherical Bessel functions in the limit eta->0.
0111  */
0112 int gsl_sf_coulomb_wave_sphF_array(double lam_min, int kmax,
0113                                         double eta, double x,
0114                                         double * fc_array,
0115                                         double * F_exponent
0116                                         );
0117
0118
0119 /* Coulomb wave function normalization constant.
0120  * [Abramowitz+Stegun 14.1.8, 14.1.9]
0121  */
0122 int gsl_sf_coulomb_CL_e(double L, double eta, gsl_sf_result * result);
0123 int gsl_sf_coulomb_CL_array(double Lmin, int kmax, double eta, double * cl);
0124
0125
0126 __END_DECLS
0127
0128 #endif /* __GSL_SF_COULOMB_H__ */