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## [Bug-gsl] Re: double gsl_sf_hydrogenicR

**From**: |
Brian Gough |

**Subject**: |
[Bug-gsl] Re: double gsl_sf_hydrogenicR |

**Date**: |
Mon, 27 Feb 2006 17:28:58 +0000 |

Alexei Meremianin writes:
>* 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?*
Thanks for bug report. The factor of r^l in the (2Z/n)^l term was
missing from the documentation. The functions are correct.
--
best regards,
Brian Gough
Network Theory Ltd,
Publishing the GSL Manual --- http://www.network-theory.co.uk/gsl/manual/

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**[Bug-gsl] Re: double gsl_sf_hydrogenicR**,
*Brian Gough* **<=**