Double Integration involving Struve and Neumann functions
- To: mathgroup at smc.vnet.net
- Subject: [mg79624] Double Integration involving Struve and Neumann functions
- From: Sooraj R <soorajrnambiar at yahoo.com>
- Date: Tue, 31 Jul 2007 06:14:51 -0400 (EDT)
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
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