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>*Reply-to*: kuska at informatik.uni-leipzig.de

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 ?? Please post your code in correct syntax .. Than try a single integral and if Mathematica does not find it read carefull http://www.amazon.de/Table-Integrals-Products-Academic-Press/dp/0123736374/ref=sr_1_1/028-4565458-4869346?ie=UTF8&s=books-intl-de&qid=1185884008&sr=1-1 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. > Many thanks in advance > 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 > >