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<a name="Normalized-Hydrogenic-Bound-States"></a>
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Next: <a rel="next" accesskey="n" href="Coulomb-Wave-Functions.html#Coulomb-Wave-Functions">Coulomb Wave Functions</a>,
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Up: <a rel="up" accesskey="u" href="Coulomb-Functions.html#Coulomb-Functions">Coulomb Functions</a>
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<h4 class="subsection">7.7.1 Normalized Hydrogenic Bound States</h4>
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— Function: double <b>gsl_sf_hydrogenicR_1</b> (<var>double Z, double r</var>)<var><a name="index-gsl_005fsf_005fhydrogenicR_005f1-389"></a></var><br>
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— Function: int <b>gsl_sf_hydrogenicR_1_e</b> (<var>double Z, double r, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fhydrogenicR_005f1_005fe-390"></a></var><br>
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<blockquote><p>These routines compute the lowest-order normalized hydrogenic bound
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state radial wavefunction <!-- {$R_1 := 2Z \sqrt{Z} \exp(-Z r)$} -->
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R_1 := 2Z \sqrt{Z} \exp(-Z r).
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</p></blockquote></div>
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— Function: double <b>gsl_sf_hydrogenicR</b> (<var>int n, int l, double Z, double r</var>)<var><a name="index-gsl_005fsf_005fhydrogenicR-391"></a></var><br>
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— Function: int <b>gsl_sf_hydrogenicR_e</b> (<var>int n, int l, double Z, double r, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fhydrogenicR_005fe-392"></a></var><br>
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<blockquote><p>These routines compute the <var>n</var>-th normalized hydrogenic bound state
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where L^a_b(x) is the generalized Laguerre polynomial (see <a href="Laguerre-Functions.html#Laguerre-Functions">Laguerre Functions</a>).
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The normalization is chosen such that the wavefunction \psi is
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<!-- {$\psi(n,l,r) = R_n Y_{lm}$} -->
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\psi(n,l,r) = R_n Y_{lm}.
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</p></blockquote></div>
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