       Re: Double Integration involving Struve and Neumann functions

• To: mathgroup at smc.vnet.net
• Subject: [mg79633] Re: Double Integration involving Struve and Neumann functions
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 1 Aug 2007 04:50:15 -0400 (EDT)
• Organization: Uni Leipzig
• References: <f8n2v8\$lsl\$1@smc.vnet.net>

```Hi,

and that phi(ze) is not the proper Mathematica syntax and you mean

psi[ze_]:=Sqrt[2/Le] Cos[(Pi ze)/Le];
psi[zh_]:=Sqrt[2/Lh] Cos[(Pi zh)/Lh];

does not matter ??

Than try a single integral and if Mathematica does not find it

if this does not help try some approximation method using series
expansions ..

Regards
Jens
Sooraj R wrote:
> Hi all
> I need to evaluate an integral of the form given below
>
> Eb=hbar^2/(2 mu R^2) - 4 charge^2/(epsilon R^2)
> Integrate[(psi(ze))^2 (psi(zh))^2 (Abs[ze - zh])
> ((Pi/2) (H1[2 Abs[(ze - zh)]/R] -
>            Nu1[2 Abs[(ze - zh)]/R]) - 1), {ze, -Le/2,
> Le/2}, {zh, -Lh/2,
>    Lh/2}]
>
> I define
> Eb=Table[0,{16}];
> charge = 1.602 10^-19;
> hbar = 1.054571 10^-34;
> m0 = 9.1019 10^-31;
> mu=0.05 m0;
> epsilon=8.85418 10^-12
> Le =
> {100,105,110,115,120,125,130,135,140,145,150,155,160,165,170};
> Lh =
> {82,87,92,97,102,107,112,117,122,127,132,137,142,147,152,157};
>
> psi(ze)=Sqrt[2/Le] Cos[(Pi ze)/Le]; and
> psi(zh)=Sqrt[2/Lh] Cos[(Pi zh)/Lh];
> are the wave functions of the system.
> R is a parameter and here it can be treated as a
> constant.(anyway the result will be a function of R)
>
> Le and Lh consists of lists..each having 16 values.
> I need to evaluate the integral for these 16 values of
> Le and Lh.
> H1 and Nu1 are the first order Struve functions and
> Neumann functions.
> For ze, the limit of integration is from -Le/2 to Le/2
> and for zh, the limit is from -Lh/2 to Lh/2.
>
> I coded the integral as follows.
>
>
> For[i = 1, 1 < 17, i++,
>  Eb[[i]] =
>   hbar^2/(2 mu R^2) -
>    4 charge^2/(epsilon R^2) Integrate[(Sqrt[
>           2/Le[[i]]] Cos[(Pi ze)/Le[[i]]])^2 (Sqrt[
>           2/Lh[[i]]] Cos[(Pi zh)/Lh[[i]]])^2 (Abs[
>         ze - zh]) ((Pi/2) (StruveH[1, 2 Abs[(ze -
> zh)]/R] -
>            BesselY[1, 2 Abs[(ze - zh)]/R]) - 1), {ze,
> -Le[[i]]/2,
>       Le[[i]]/2}, {zh, -Lh[[i]]/2, Lh[[i]]/2} // N]]
>
>
> Mathematica was evaluating it for almost two
> days...and I had to quit the kernel to stop it.(Abort
> evaluation was not working out)
>
> I was thinking the problem is because of the For loop,
> so decided to check whether it is able to evaluate for
> a particular value of Le and Lh.
>
> To my sorrow, I found that after running for almost 24
> hrs, mathematica returned the integral unevaluated.
>
> Can someone help me how to solve this integral?. The
> Cosine wave functions are the simplest case, and I
> need to calculate Eb for systems having Airy functions
> as the wavefunctions, and I'm scared to imagine such a
> situation.
>
> Any help is deeply appreciated.
> Best regards
>
> Sooraj
>
>
>
>
>
>
>       ____________________________________________________________________________________
> Fussy? Opinionated? Impossible to please? Perfect.  Join Yahoo!'s user panel and lay it on us. http://surveylink.yahoo.com/gmrs/yahoo_panel_invite.asp?a=7
>
>

```

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