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Re: Integral of radial solution (hydrogen atom) is not evaluated

• To: mathgroup at smc.vnet.net
• Subject: [mg91535] Re: Integral of radial solution (hydrogen atom) is not evaluated
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Mon, 25 Aug 2008 06:57:15 -0400 (EDT)
• Organization: Uni Leipzig
• References: <g8lp87$ih2$1@smc.vnet.net> <g8o85j$l6c$1@smc.vnet.net> <g8tsq9$nv0$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de

Hi,

I don't know, but I expect that Mathematica uses
a "special extension" of Laguerre polynomials
Try

Plot3D[
  LaguerreL[n, l, 1], {n, 0, 5}, {l, 0, 5}]

For this special extension (real n and real l and l>n)
the orthogonal relation does not hold.

Regards
   Jens

Gehricht at googlemail.com wrote:
> Hi!
> 
>> and Mathematica can't evaluate
>> Integrate[
>>   LaguerreL[n1, l1, r]*LaguerreL[n2, l2, r]*Exp[-r], {r, 0, Infinity}]
>>
>> or
>>
>> Integrate[
>>   LaguerreL[n, l, r]*LaguerreL[n, l, r]*Exp[-r], {r, 0, Infinity}]
> 
> Is there any special reason for that?
> But thank you for the information!
> With thanks
> Wolfgang
> 

• Follow-Ups:
  • RE: Re: Integral of radial solution (hydrogen atom) is not evaluated
    • From: "Tony Harker" <a.harker@ucl.ac.uk>