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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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