**Stephen P. King** (*stephenk1@home.com*)

*Mon, 22 Mar 1999 08:20:05 -0500*

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Dear Hitoshi,

I'm looking into the n-body problem:

http://www-cicma.concordia.ca/faculty/rhall/mbp.html#top

"Many-body problems in quantum mechanics

An important idea used in our approach to the many-body problem is

to exploit the non-individuality of identical particles to relate the

N-body problem to certain specially constructed 2-body problems. We

study systems of N identical particles bound by pair potentials. We let

H be the Hamiltonian for the system, with the centre-of-mass KE removed.

Since the symmetrization postulate (for bosons or fermions) is in

the individual particle indices, the expression of the Bose or Fermi

symmetry in the translation-invariant many-body wave function may be

quite complicated. In suitable units, and for either species of

particle, we have <H> = (N-1)<K + (N/2)V>, where K and V are (reduced)

two-body operators. Thus there is a close relation between H/(N-1) and

the corresponding (reduced) two-body Hamiltonian H = K + (N/2)V. This

relation allows one to derive general lower-bound energy formulas for

the N-body problem: for strongly bound systems, these lower bounds are

often surprisingly good; for harmonic oscillators, they may be exact. In

the case of fermions, the attempt to express the anti-symmetry of the

many-body wave function in expansions over two-body states leads to the

use of non-orthogonal relative coordinates. These methods can also be

applied to the excited N-body states."

I sent Dr. Richard L. Hall

(http://www-cicma.concordia.ca/faculty/rhall/rhall.html#top) e-mail

asking for a copy of his paper: Spectral geometry and the N-body

problem, Richard L. Hall Phys. Rev. A 51, 3499-3505 (1995).

Looking further, I do remember that Prigogine's work is motivated by the

problem of computing n-body minimizations...

Later,

Stephen

**Next message:**Stephen P. King: "[time 45] n-body dirac equation"**Previous message:**Matti Pitkanen: "[time 43] RE: The ordering of spatial states and temporalevents"

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