1\name{Coulomb} 2\alias{Coulomb} 3\alias{coulomb} 4\alias{hydrogenicR_1} 5\alias{hydrogenicR} 6\alias{coulomb_wave_FG} 7\alias{coulomb_wave_F_array} 8\alias{coulomb_wave_FG_array} 9\alias{coulomb_wave_FGp_array} 10\alias{coulomb_wave_sphF_array} 11\alias{coulomb_CL} 12\alias{coulomb_CL_array} 13\title{Coulomb functions} 14\description{ 15 Coulomb functions as per the Gnu Scientific Library, reference manual 16 section 7.7 and AMS-55, chapter 14. These functions are declared 17 in header file \code{gsl_sf_coulomb.h} 18} 19\usage{ 20hydrogenicR_1(Z, r, give=FALSE, strict=TRUE) 21hydrogenicR(n, l, Z, r, give=FALSE, strict=TRUE) 22coulomb_wave_FG(eta, x, L_F, k, give=FALSE, strict=TRUE) 23coulomb_wave_F_array(L_min, kmax, eta, x, give=FALSE,strict=TRUE) 24coulomb_wave_FG_array(L_min, kmax, eta, x, give=FALSE,strict=TRUE) 25coulomb_wave_FGp_array(L_min, kmax, eta, x, give=FALSE,strict=TRUE) 26coulomb_wave_sphF_array(L_min, kmax, eta, x, give=FALSE,strict=TRUE) 27coulomb_CL(L,eta, give=FALSE,strict=TRUE) 28coulomb_CL_array(L_min, kmax, eta, give=FALSE,strict=TRUE) 29} 30\arguments{ 31 \item{n,l,kmax}{input: integers} 32 \item{Z,r,eta,x,L_F,L_min,k,L}{input: real values} 33 \item{give}{Boolean with \code{TRUE} meaning to return a list of three 34 items: the value, an estimate of the error, and a status number} 35 \item{strict}{Boolean, with \code{TRUE} meaning to return \code{NaN} 36 if status is an error} 37} 38\references{\url{https://www.gnu.org/software/gsl/}} 39\author{Robin K. S. Hankin} 40\examples{ 41 42x <- seq(from=0,to=14,len=300) 43jj <- coulomb_wave_FG(1,10,x,0) 44plot(x,jj$val_F,type="l",xaxt="n",yaxt="n",bty="n",xlab="",ylab="", 45 main="Figure 14.1, p539") 46lines(x,jj$val_G,type="l",lty=2) 47axis(1,pos=0,at=1:14, 48 labels=c("","2","","4","","6","","8","","10","","12","","14")) 49lines(c(0,1),c(0,0)) 50axis(2,pos=0) 51text(9.5, 0.63, expression(F[L])) 52text(8.5, 1.21, expression(G[L])) 53 54 55 56 57 58x <- seq(from=0,to=24,len=400) 59plot(x,coulomb_wave_FG(eta=1,x,L_F=0,k=0)$val_F,type="l", 60 ylim=c(-1.3,1.7), xlim=c(0,26), 61 xaxt="n",yaxt="n",bty="n",xlab="",ylab="",main="Figure 14.3, p541",lty=3) 62lines(x,coulomb_wave_FG(eta= 0,x,L_F=0,k=0)$val_F,type="l",lty=1) 63lines(x,coulomb_wave_FG(eta= 5,x,L_F=0,k=0)$val_F,type="l",lty=6) 64lines(x,coulomb_wave_FG(eta=10,x,L_F=0,k=0)$val_F,type="l",lty=6) 65lines(x,coulomb_wave_FG(eta=x/2,x,L_F=0,k=0)$val_F,type="l",lty="F3") 66axis(1,pos=0,at=1:24, 67 labels=c("","2","","4","","","","8","","10","","12", 68 "","14","","","","18","","","","22","","24")) 69lines(c(0,26),c(0,0)) 70axis(2,pos=0,at=0.2*(-6:9), 71 labels=c("","-1.2","","-.8","","-.4","","0","",".4", 72 "",".8","","1.2","","1.6")) 73text(2.5, -0.8, expression(eta == 0)) 74text(4.5,1.1,adj=0, expression(eta == 1)) 75text(14,1.4,adj=0, expression(eta == 5)) 76text(22,1.4,adj=0, expression(eta == 10)) 77 78 79 80 81 82 83x <- seq(from=0.5,to=10,by=0.5) 84jj <- coulomb_wave_FG(eta=t(matrix(x,20,5)), x=1:5,0,0) 85jj.F <- t(jj$val_F) 86jj.G <- t(jj$val_G) 87colnames(jj.F) <- 1:5 88colnames(jj.G) <- 1:5 89cbind(x,jj.F) #table 14.1, p 546, top bit. 90cbind(x,jj.G) #table 14.1, p 547, top bit. 91 92 93 94} 95 96\keyword{array} 97