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

• To: mathgroup at smc.vnet.net
• Subject: [mg91542] RE: [mg91535] Re: Integral of radial solution (hydrogen atom) is not evaluated
• From: "Tony Harker" <a.harker at ucl.ac.uk>
• Date: Tue, 26 Aug 2008 03:29:36 -0400 (EDT)
• References: <g8lp87$ih2$1@smc.vnet.net> <g8o85j$l6c$1@smc.vnet.net> <g8tsq9$nv0$1@smc.vnet.net> <200808251057.GAA27369@smc.vnet.net>

Yes, but even with appropriate Assumptions Mathematica does not produce the
correct forms.

  Tony

]-> -----Original Message-----
]-> From: Jens-Peer Kuska [mailto:kuska at informatik.uni-leipzig.de] 
]-> Sent: 25 August 2008 11:57
]-> To: mathgroup at smc.vnet.net
]-> Subject: [mg91535] Re: Integral of radial solution 
]-> (hydrogen atom) is not evaluated
]-> 
]-> 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
]-> > 
]-> 
]-> 

• References:
  • Re: Integral of radial solution (hydrogen atom) is not evaluated
    • From: Jens-Peer Kuska <kuska@informatik.uni-leipzig.de>