Re: Different Integration Results
- To: mathgroup at smc.vnet.net
- Subject: [mg30366] Re: [mg30344] Different Integration Results
- From: BobHanlon at aol.com
- Date: Sun, 12 Aug 2001 02:29:54 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 2001/8/11 4:38:06 AM, Harald.Grossauer at uibk.ac.at writes:
>I have got a problem with the attached notebook. In the last two lines,
>if I use Integrate[ ] the result is 99/35, NIntegrate[ ] says it is
>"1.". Due to the nature of the problem (quantum theory, fourier
>transform) I would expect the result to be 1 exactly. What could cause
>this difference?
>
Use FullSimplify when evaluating psi and psiconj. The form of the rho is
then very simple and integrating rho works fine.
phi[p_]:= Evaluate[Simplify[
18/Sqrt[35]*UnitStep[p]*p*(Exp[-p]-(1/6)*Exp[-p/2])]];
Integrate[phi[p]^2,{p,-Infinity,Infinity}]
1
psi[x_]:=Evaluate[FullSimplify[
(1/Sqrt[2*Pi])*Integrate[phi[p]*Exp[I*p*x],
{p,-Infinity,Infinity}],Element[x,Reals]]];
psiconj[x_]:= Evaluate[FullSimplify[
(1/Sqrt[2*Pi])*Integrate[phi[p]*Exp[-I*p*x],
{p,-Infinity,Infinity}],Element[x,Reals]]];
rho[x_]:= Evaluate[Simplify[psi[x]*psiconj[x]]];
Plot[rho[x],{x,-10,10}];
Integrate[rho[x],{x,-Infinity,Infinity}]
1
NIntegrate[rho[x],{x,-Infinity,Infinity}]
0.9999999999999989
Bob Hanlon
Chantilly, VA USA