Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2001
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2001

[Date Index] [Thread Index] [Author Index]

Search the Archive

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


  • Prev by Date: Re: using findroot for multiple functions
  • Next by Date: RE: using findroot for multiple functions
  • Previous by thread: Different Integration Results
  • Next by thread: Re: Different Integration Results