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MathGroup Archive 2001

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Re: Any quantum chemists / physicists?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg30241] Re: Any quantum chemists / physicists?
  • From: "Alan Mason" <amason2 at austin.rr.com>
  • Date: Fri, 3 Aug 2001 00:56:11 -0400 (EDT)
  • References: <9k5r6g$hc1$1@smc.vnet.net> <9k88k4$52q$1@smc.vnet.net> <9kavv6$c3d$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hello,
I don't know of any books dealing specifically with the pattern matcher.
There are several volumes by Maeder (one of the three original developers of
Mathematica) that cover packages and certain other things well, but not the
pattern matcher per se.  The Mathematica Book by Wolfram has essential
material on pattern matching but lacks in-depth coverage.  So far I have
successfully resisted the idea of writing a book myself specifically to fill
this gap, based on my own experience with the pattern matcher; after all,
Wolfram himself could do this much better. The trouble with the pattern
matcher is that by its nature it can deal only with syntax (the form of
expressions), not semantics (mathematical meaning).  Since expressions with
different forms can be mathematically equivalent,  there is some unavoidable
tension between it and the rest of Mathematica.  That is, the pattern
matcher forces you to know how Mathematica represents expressions internally
before you can do much of anything with it (that's why FullForm[] is so
important), and you need to be able to rely on Mathematica to always use the
same form consistently.  Wolfram Research is sensitive to complaints from
users about Mathematica changing the form of their input, thereby making
their patterns fail, especially when Mathematica itself is inconsistent in
how it changes the input.  I remember giving them hell about this a few
years ago; in my application I had to have precise control over the form of
my expressions, but Mathematica kept changing things in an inconsistent way.
However, version 4.1 is much improved.

You should be able to learn what you need by experimenting with Mathematica
and seeing why patterns you were sure would match sometimes in fact don't.
Write some code dealing with specific small tasks you need to perform in
your applications and check that everything works the way you expect.  Using
FullForm[], observe how Mathematica represents Minus and Divide in term of
Plus (with Times) and Times (with Power); that -3 is an atom and will not
match the pattern -x_, etc. You'll have some surprises, but rest assured --
everything can be made to work, and fairly predictably.  Save your notebooks
so you don't forget what you've learned (I have a whole Teach subdirectory);
you'll want to refer to them if you start a project when you haven't used
Mathematica in awhile.

Many users feel that Mathematica is badly designed in the sense that not
only is it not user friendly, but the reasons for why it does what it does
are unclear and mostly undocumented.  But as I have learned the system
better, I have come around to the view that it is indeed beautifully
conceived and well suited for demanding scientific applications.  There are
good reasons for why it behaves as it does (efficiency and generality), and
it strives for power and generality even if this means a steep learning
curve.

Alan
----- Original Message -----
From: "Gustavo Seabra" <gseabra at swbell.net>
To: mathgroup at smc.vnet.net
Subject: [mg30241] Re: Any quantum chemists / physicists?


> Thanks. At least now I know what to do. Are there any books / web sites
with
> useful information you could recommend?
>
>     Gustavo.
>
>
> "Alan Mason" <amason2 at austin.rr.com> wrote in message
> news:9k88k4$52q$1 at smc.vnet.net...
> > Hello,
> > I am interested in computational quantum chemistry and have written
> > Mathematica code to handle differential operator calculus, commutators,
> etc.
> > I use it as a tool to spit out "exact" rotational-vibrational
Hamiltonians
> > for simple molecules; see, e.g., the paper by Bramley et al., Molec.
> Phys.,
> > Vol. 73 (1991), pp. 1183-1208.  I also have some Mathematica code for
> > checking the calculations on pp. 419-423 of the book Quantum Field
Theory
> by
> > Itzykson and Zuber; this code is the core of a QFT package that I'll
> > probably never write.  By the way, I do not get their result.  (In any
> case,
> > it was sheer madness on their part to include such a beastly calculation
> in
> > what is supposed to be a graduate text on QFT!!)
> >
> > There is information about differential operator calculus in the
> Mathematica
> > Archives, and you might want to search there.  I don't know if any
> genuinely
> > useful full-blown commercial QFT package exists, even though Mathematica
> was
> > originally created to assist in just this field.  Has anyone has ever
used
> > such a package to answer a nontrivial QFT problem, such as computing the
> > Lamb shift through order 4 in alpha, say?  Here I mean "used in a
> systematic
> > way with little or no human intervention" --  not just computing a whole
> > bunch of QFT integrals piecemeal.  A few months ago I downloaded some
code
> > from a web site that used to be linked to the Mathematica site, but I
> found
> > it to be buggy and not useful.
> >
> >  It's difficult to write good general commercial packages that give
useful
> > results for whole classes of significant problems.  Any such package is
> > likely to be expensive, as it is hard to develop, it's specialized, and
> > there won't be many users.  (Of course, Wolfram Research has already
taken
> > care of integration and ordinary differential equations.) So it's
probably
> > best to write your own code, tailored to your particular application.
To
> > do this you'll need to thoroughly understand the pattern matcher, which
> will
> > take some study.  I have found the effort very worthwhile.
> > "Gustavo Seabra" <gseabra at swbell.net> wrote in message
> > news:9k5r6g$hc1$1 at smc.vnet.net...
> > > Hello,
> > >
> > >     Are there any quantum chemists / physicists around using
> Mathematica?
> > I
> > > was wondering if there is any package that handles things like
> > commutators,
> > > operators algebra, second quantization, superoperators, etc...
> > >
> > > Thanks,
> > > --
> > > -----------------------------------------------------------------
> > > Gustavo Seabra - Graduate Student
> > > Chemistry Department
> > > Kansas State University
> > > -----------------------------------------------------------------
> > >
> > >
> >
> >
> >
>
>
"Gustavo Seabra" <gseabra at swbell.net> wrote in message
news:9kavv6$c3d$1 at smc.vnet.net...
> Thanks. At least now I know what to do. Are there any books / web sites
with
> useful information you could recommend?
>
>     Gustavo.
>
>
> "Alan Mason" <amason2 at austin.rr.com> wrote in message
> news:9k88k4$52q$1 at smc.vnet.net...
> > Hello,
> > I am interested in computational quantum chemistry and have written
> > Mathematica code to handle differential operator calculus, commutators,
> etc.
> > I use it as a tool to spit out "exact" rotational-vibrational
Hamiltonians
> > for simple molecules; see, e.g., the paper by Bramley et al., Molec.
> Phys.,
> > Vol. 73 (1991), pp. 1183-1208.  I also have some Mathematica code for
> > checking the calculations on pp. 419-423 of the book Quantum Field
Theory
> by
> > Itzykson and Zuber; this code is the core of a QFT package that I'll
> > probably never write.  By the way, I do not get their result.  (In any
> case,
> > it was sheer madness on their part to include such a beastly calculation
> in
> > what is supposed to be a graduate text on QFT!!)
> >
> > There is information about differential operator calculus in the
> Mathematica
> > Archives, and you might want to search there.  I don't know if any
> genuinely
> > useful full-blown commercial QFT package exists, even though Mathematica
> was
> > originally created to assist in just this field.  Has anyone has ever
used
> > such a package to answer a nontrivial QFT problem, such as computing the
> > Lamb shift through order 4 in alpha, say?  Here I mean "used in a
> systematic
> > way with little or no human intervention" --  not just computing a whole
> > bunch of QFT integrals piecemeal.  A few months ago I downloaded some
code
> > from a web site that used to be linked to the Mathematica site, but I
> found
> > it to be buggy and not useful.
> >
> >  It's difficult to write good general commercial packages that give
useful
> > results for whole classes of significant problems.  Any such package is
> > likely to be expensive, as it is hard to develop, it's specialized, and
> > there won't be many users.  (Of course, Wolfram Research has already
taken
> > care of integration and ordinary differential equations.) So it's
probably
> > best to write your own code, tailored to your particular application.
To
> > do this you'll need to thoroughly understand the pattern matcher, which
> will
> > take some study.  I have found the effort very worthwhile.
> > "Gustavo Seabra" <gseabra at swbell.net> wrote in message
> > news:9k5r6g$hc1$1 at smc.vnet.net...
> > > Hello,
> > >
> > >     Are there any quantum chemists / physicists around using
> Mathematica?
> > I
> > > was wondering if there is any package that handles things like
> > commutators,
> > > operators algebra, second quantization, superoperators, etc...
> > >
> > > Thanks,
> > > --
> > > -----------------------------------------------------------------
> > > Gustavo Seabra - Graduate Student
> > > Chemistry Department
> > > Kansas State University
> > > -----------------------------------------------------------------
> > >
> > >
> >
> >
> >
>
>



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