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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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