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[Bug-gsl] double gsl_sf_hydrogenicR

From: Alexei Meremianin
Subject: [Bug-gsl] double gsl_sf_hydrogenicR
Date: 24 Feb 2006 11:14:40 +0100
User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.3

Dear Brian,

I have a big problem.
 According to the info file for the gsl-1.6

 - Function: double gsl_sf_hydrogenicR (int N, int L, double Z, double
 - Function: int gsl_sf_hydrogenicR_e (int N, int L, double Z, double
          R, gsl_sf_result * RESULT)
     These routines compute the N-th normalized hydrogenic bound state
     radial wavefunction,
          R_n := 2 (Z^{3/2}/n^2) \sqrt{(n-l-1)!/(n+l)!} \exp(-Z r/n) (2Z/n)^l
                    L^{2l+1}_{n-l-1}(2Z/n r).

     The normalization is chosen such that the wavefunction \psi is
     given by \psi(n,l,r) = R_n Y_{lm}.


However, as follows from the Book Landau&Lifshitz, "Quantum mechanics",
Pergamon press,
the factor r^l is missing in the above definition of the radial function R_n.
 Could you comment on that.
Is it a bug or feature? Or Laguerre polynomials are defined differently?

with best regards,
 Alexei Meremianin

 Research Fellow,
 Max Planck Institute for the Physics of Complex Systems,
 Noethnitzer Str 38, 01187 Dresden, Germany,
   Phone: +49 351 871-2411
   Fax: +49 351 871-1999

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