       Re: Double integral of a piecewise-constant function

• To: mathgroup at smc.vnet.net
• Subject: [mg61447] Re: [mg61395] Double integral of a piecewise-constant function
• From: Chris Chiasson <chris.chiasson at gmail.com>
• Date: Wed, 19 Oct 2005 02:16:49 -0400 (EDT)
• References: <200510180644.CAA11181@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Sometimes Mathematica refuses to do things because it assumes all
symbols could be complex. I didn't look at your integral, but I was
wondering if you made any assumptions on the domain or range of any of
the symbols when you did the integration by hand. Also, others might

On 10/18/05, Chris Rodgers <rodgers at physchem.nospamox.aremovec.uk> wrote:
> Dear All,
>
> I am trying to use Mathematica to calculate some quantum mechanical
> expressions involving integrals of commutators. In the simplest case,
> the Hamiltonian of the system is piecewise constant.
>
> My problem is that Mathematica can integrate this expression:
>
> (-(1/2))*Integrate[Piecewise[{{0, t < 0 || t >= 3 || (t < 1 &&
> t < 1) || (t < 2 && t >= 3) || (t >= 1 && t < 0) ||
>          (Inequality[1, LessEqual, t, Less, 2] && Inequality[1,
> LessEqual, t, Less, 2]) || (t >= 2 && t >= 2)},
>        {Comm[Subscript[H, 1], Subscript[H, 2]], t < 1 && t < 2},
> {Comm[Subscript[H, 1], Subscript[H, 3]], t < 1},
>        {Comm[Subscript[H, 2], Subscript[H, 1]], t < 2 && t < 1},
> {Comm[Subscript[H, 2], Subscript[H, 3]], t < 2},
>        {Comm[Subscript[H, 3], Subscript[H, 1]], t < 1}},
> Comm[Subscript[H, 3], Subscript[H, 2]]] /. t -> 0, {t, 0, 3}]
>
> but it can't do the two dimension integral of the same expression:
>
> -Integrate[Integrate[Piecewise[{{0, t < 0 || t >= 3 || (t < 1
> && t < 1) || (t < 2 && t >= 3) || (t >= 1 && t < 0) ||
>          (Inequality[1, LessEqual, t, Less, 2] && Inequality[1,
> LessEqual, t, Less, 2]) || (t >= 2 && t >= 2)},
>        {Comm[Subscript[H, 1], Subscript[H, 2]], t < 1 && t < 2},
> {Comm[Subscript[H, 1], Subscript[H, 3]], t < 1},
>        {Comm[Subscript[H, 2], Subscript[H, 1]], t < 2 && t < 1},
> {Comm[Subscript[H, 2], Subscript[H, 3]], t < 2},
>        {Comm[Subscript[H, 3], Subscript[H, 1]], t < 1}},
> Comm[Subscript[H, 3], Subscript[H, 2]]], {t, 0, t}], {t, 0, 3}]/2
>
> To me these look pretty similar, and both are easy to do with pencil and
> paper. How should I set things up so that Mathematica can perform the
> second integral?
>
> Many thanks,
>
> Chris.
>
>

--
Chris Chiasson
http://chrischiasson.com/contact/chris_chiasson

```

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