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MathGroup Archive 2004

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Re: Fourier analysis with additional coefficient for the R-matirx

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48507] Re: Fourier analysis with additional coefficient for the R-matirx
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Fri, 4 Jun 2004 04:49:21 -0400 (EDT)
  • Organization: The University of Western Australia
  • References: <c9k3l0$fdm$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <c9k3l0$fdm$1 at smc.vnet.net>, "Mars" <MarsJO at pentech.ac.za> 
wrote:

> I have simplified the R-matrix theory for calculating cross sections.
> In the equation y, Ci (i=0..2) and u are functions of x and can all be
> calculated.
> The equation is
>      
> y(x)=C0(x)+Sum(Bl*C1(x)Pl)+Sum(Tl*C2(x)Pl*cos(u(x)))+Sum(Rl(-C2(x)Pl*sin(u(x)))

This expression is ambiguous:

[1] Do C1(x) and C2(x) depend on l (if not, bring outside the summation)?

[2] Does u(x) depend on l (if not, bring outside the summation)?
 
> The summation is from l=0..infinity and Pl is the (cosine of the)
> Legendre polynomial.

[3] You mean that the argument of Pl is the cosine of an angle? Is the 
angle the same for the transmitted and reflected partial waves? If so, 
then y is not just a function of x.

> This is a Fourier series analysis, with the exclusion of the second
> term, and can easily be solved 
> for Tl and Rl with mathematica.
> However, I would like to know how one can solve all three Bl, Tl and
> Rl.

Why not write your expression _explicitly_ (in Mathematica notation is a 
good choice), indicating all functional and parameter dependencies? For 
example,

   Sum[b[l] C[1][l][x] LegendreP[l, Cos[Theta[1]]],{l,0,Infinity}]

is quite clear. Otherwise it is difficult or impossible to answer the 
question you pose.

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)         
35 Stirling Highway
Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul


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