DiracDelta Integrals

• To: mathgroup at smc.vnet.net
• Subject: [mg9185] DiracDelta Integrals
• From: Peter Jay Salzman <psalzman at landau.ucdavis.edu>
• Date: Tue, 21 Oct 1997 02:02:58 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```dear mathgroup,

just out of curiosity, i tried

Integrate[ Exp[I k x], {x, -Infinity, Infinity}]

and Mathematica said "the integral is 0 if Im[k]==0, otherwise, i give
up".   so, thinking i was being slick, i loaded the
Calculus`DiracDelta` package.

i tried the integral again, but Mathematica said the same thing.  then,
knowing that this comes up all the time in fourier transforms, i loaded
Calculus`FourierTransform`.  this time, when i entered the integral,
Mathematica told me:  "hey, bubba.  that integral doesn't converge on
the domain of integration".

surely, there MUST be a package that allows Mathematica to do this
integral and give me 2 Pi DiracDelta[k].  what do i need to load to
make Mathematica recognize this?

the reason why i'm asking is because i'm trying to do the integral

Exp[-Abs[k]/c] Exp[I k x]  Exp[i p x/hbar], {x,-Infinity,Infinity},

{k, -Infinity, Infinity}

by the way, are there any packages that allow bra-ket notation on
Mathematica? i would find it hard to believe that Mathematica has the
RiemannSiegelTheta function but couldn't compute something like <f|f>.

peter

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```

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