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- /* specfunc/coulomb_bound.c
- *
- * 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 3 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 */
- #include "gsl__config.h"
- #include "gsl_math.h"
- #include "gsl_errno.h"
- #include "gsl_sf_exp.h"
- #include "gsl_sf_gamma.h"
- #include "gsl_sf_pow_int.h"
- #include "gsl_sf_laguerre.h"
- #include "gsl_sf_coulomb.h"
- #include "gsl_specfunc__error.h"
- #include "gsl_specfunc__check.h"
- /* normalization for hydrogenic wave functions */
- static
- int
- R_norm(const int n, const int l, const double Z, gsl_sf_result * result)
- {
- double A = 2.0*Z/n;
- double pre = sqrt(A*A*A /(2.0*n));
- gsl_sf_result ln_a, ln_b;
- gsl_sf_result ex;
- int stat_a = gsl_sf_lnfact_e(n+l, &ln_a);
- int stat_b = gsl_sf_lnfact_e(n-l-1, &ln_b);
- double diff_val = 0.5*(ln_b.val - ln_a.val);
- double diff_err = 0.5*(ln_b.err + ln_a.err) + GSL_DBL_EPSILON * fabs(diff_val);
- int stat_e = gsl_sf_exp_err_e(diff_val, diff_err, &ex);
- result->val = pre * ex.val;
- result->err = pre * ex.err;
- result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
- return GSL_ERROR_SELECT_3(stat_e, stat_a, stat_b);
- }
- /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
- int
- gsl_sf_hydrogenicR_1_e(const double Z, const double r, gsl_sf_result * result)
- {
- if(Z > 0.0 && r >= 0.0) {
- double A = 2.0*Z;
- double norm = A*sqrt(Z);
- double ea = exp(-Z*r);
- result->val = norm*ea;
- result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val) * fabs(Z*r);
- CHECK_UNDERFLOW(result);
- return GSL_SUCCESS;
- }
- else {
- DOMAIN_ERROR(result);
- }
- }
- int
- gsl_sf_hydrogenicR_e(const int n, const int l,
- const double Z, const double r,
- gsl_sf_result * result)
- {
- if(n < 1 || l > n-1 || Z <= 0.0 || r < 0.0) {
- DOMAIN_ERROR(result);
- }
- else {
- double A = 2.0*Z/n;
- gsl_sf_result norm;
- int stat_norm = R_norm(n, l, Z, &norm);
- double rho = A*r;
- double ea = exp(-0.5*rho);
- double pp = gsl_sf_pow_int(rho, l);
- gsl_sf_result lag;
- int stat_lag = gsl_sf_laguerre_n_e(n-l-1, 2*l+1, rho, &lag);
- double W_val = norm.val * ea * pp;
- double W_err = norm.err * ea * pp;
- W_err += norm.val * ((0.5*rho + 1.0) * GSL_DBL_EPSILON) * ea * pp;
- W_err += norm.val * ea * ((l+1.0) * GSL_DBL_EPSILON) * pp;
- result->val = W_val * lag.val;
- result->err = W_val * lag.err + W_err * fabs(lag.val);
- result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
- if ((l == 0 || (r > 0 && l > 0)) && lag.val != 0.0
- && stat_lag == GSL_SUCCESS && stat_norm == GSL_SUCCESS) {
- CHECK_UNDERFLOW(result);
- };
- return GSL_ERROR_SELECT_2(stat_lag, stat_norm);
- }
- }
- /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
- #include "gsl_specfunc__eval.h"
- double gsl_sf_hydrogenicR_1(const double Z, const double r)
- {
- EVAL_RESULT(gsl_sf_hydrogenicR_1_e(Z, r, &result));
- }
- double gsl_sf_hydrogenicR(const int n, const int l, const double Z, const double r)
- {
- EVAL_RESULT(gsl_sf_hydrogenicR_e(n, l, Z, r, &result));
- }
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