Re: oh, my god, physicist are really A-holes.

On Thu, 25 Oct 2006, Igor wrote:


Eric Gisse wrote:
Timo Nieminen wrote:
On Wed, 24 Oct 2006 mainargv@xxxxxxxxx wrote:

All the textbooks and web resources I can find, started to fudge after
hydrogen, saying how difficult or complacated things are. You have to
make three simplications just to write down the equation for Helium,
not to mention figuring out suitable boundary conditions. I guess It's
impractical to solve for Helium by hand. Now if all the indrotductory
resources sound like this, what would you think? Would you have
confidence in the theory?

Why not? Helium is an N-body system; if you read a book on celestial
mechanics, and find out that N-body systems are very hard to solve for
N>2, would that cause you to lose confidence in classical mechanics and
Newtonian gravitation? If you read a book on classical electrodynamics,
and find that there only three analytical solutions [1], would that cause
you to lose confidence in classical electrodynamics?

I had an interesting conversation with one of my professors.

Solving quantum systems exactly came up, and I mentioned that I thought
Helium could be solved exactly. He explained that we can't solve Helium
exactly. The reasoning seemed to come down to the fact that it is a
multibody problem, which is just as unsolvable in QM as it is in
classical mechanics.

It was topical because I'm wondering *how* multi-body systems are
represented in QM.

Actually an exact solution to the three body case was found in 1912,
and an exact solution to the N body case in general was obtained in the
1990's. The main problem with both of these solutions is that they are
extremely slowly converging power series that are totally useless for
any realistic calculations. More can be found here:

http://en.wikipedia.org/wiki/N-body_problem

Just so. There's a reason why I wrote "very hard". But then, I do
computational physics, and I also call a computational solution a
"solution", and tend not to call an analytical series solution that
defies computation (eg, impractical convergence) a "solution". A
mathematician might disagree, but that's just a matter of "solution"
having two distinct meanings.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
.

Relevant Pages

  • Re: oh, my god, physicist are really A-holes.
    ... impractical to solve for Helium by hand. ... Helium is an N-body system; if you read a book on celestial ... would that cause you to lose confidence in classical mechanics and ... If you read a book on classical electrodynamics, ...
    (sci.physics)
  • Re: oh, my god, physicist are really A-holes.
    ... impractical to solve for Helium by hand. ... would that cause you to lose confidence in classical mechanics and ... If you read a book on classical electrodynamics, ... Actually an exact solution to the three body case was found in 1912, ...
    (sci.physics)
  • Re: oh, my god, physicist are really A-holes.
    ... add that QM is the most successful physical theory ever devised. ... All the textbooks and web resources I can find, ... impractical to solve for Helium by hand. ... First you were whining that the book was fudging. ...
    (sci.physics)
  • Re: oh, my god, physicist are really A-holes.
    ... add that QM is the most successful physical theory ever devised. ... All the textbooks and web resources I can find, ... impractical to solve for Helium by hand. ... First you were whining that the book was fudging. ...
    (sci.physics)
  • Re: oh, my god, physicist are really A-holes.
    ... add that QM is the most successful physical theory ever devised. ... All the textbooks and web resources I can find, started to fudge after ... impractical to solve for Helium by hand. ...
    (sci.physics)