RE: Fermi reference

["Dukelow, James S Jr" <jim.dukelow@pnl.gov>]

Mike Stabin wrote:

-----Original Message-----

From: Michael Stabin [mailto:michael.g.stabin@vanderbilt.edu]

Sent: Friday, December 28, 2001 5:12 PM

To: Radsafe

Subject: Fermi reference



I have seen the following statement made many times, but never substantiated

with an exact reference:



"In about 1948 Fermi, Metropolis, and Ulam obtained Monte Carlo estimates

for the eigenvalues of Schrodinger equation."



Would anyone have an actual reference that could be cited for this? Thanks

in advance.



Mike



===============



Jim Dukelow offers a semi-response:



Stan Ulam in his autobiography, Adventures of a Mathematician, Scribners, 1976,

writes that shortly after his return to Los Alamos, probably in 1946 or 47, he

gave to two seminars that "had good or lucky ideas and led to successful further

development".  One was on what became known as the Monte Carlo method.  He

describes an earlier discussion of the basic idea with John von Neumann as they

drove from Los Alamos to Lamy in a government car.  This part of the book is

vague on chronology -- the seminar may have been as late as 1948.  The

abbreviated bibliography lists one paper by Ulam on Monte Carlo, "On the Monte

Carlo Method", in Proceedings, Symposium on Large-Scale Digital Calculating

Machines, September 1949, Cambridge, Mass., Harvard University Press, 1951.



Mohtwani and Raghavan, Randomized Algorithms, Cambridge U Press, 1995, p. 24,

has the following: "Monte Carlo methods have been popular in the sciences for

over a hundred years now.  The classical experiment on approximating the value

of [pi] by dropping needles on a sheet of paper with parallel lines is described

in an eighteen-century paper by Buffon [86] (see also Hall [190]).  The origin

of the modern theory of Monte Carlo methods in the physical sciences is widely

attributed to Ulam, von Neumann, and Fermi [116]."



Reference 116 is  J.H. Curtis, Monte Carlo Method, National Bureau of Standards

Applied Mathematics Series, 12, 1951.



Gian-Carlo Rota, in a moving remembrance of Ulam, "The Lost Cafe", published in

a 1987 special issue of Los Alamos Science, writes that Ulam invited B.S.

Everett to Los Alamos, where they worked jointly on the theory of branching

processes, relevant to the initial applications of the Monte Carlo method to

neutron transport problems.



Nicholas Metropolis, in an essay, "The Age of Computing: A Personal Memoir", in

the Winter 1992 issue of Daedalus, writes, "The Monte Carlo Method, without

which computer simulations of neutron diffusion would have been impossible, was

developed by Ulam and myself without any knowledge of statistics; to this day

the theoretical statistician has been unable to give a proper foundation to the

method."



Best regards.



Jim Dukelow

Pacific Northwest National Laboratory

Richland, WA

jim.dukelow@pnl.gov



These comments are mine and have not been reviewed and/or approved by my

management or by the U.S. Department of Energy.



"The calculations are not for every reader, altho' their results can be readily

enough understood."



Thomas Jefferson, in a 21 March 1819 letter to John Adams, commenting on certain

theories of the stability of planetary orbits.