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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
R)
- 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

**[Bug-gsl] double gsl_sf_hydrogenicR**,
*Alexei Meremianin* **<=**