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Douglas Hartree and Early Compulations in Quantum Mechanics

IP.com Disclosure Number: IPCOM000129553D
Original Publication Date: 1988-Mar-31
Included in the Prior Art Database: 2005-Oct-06
Document File: 9 page(s) / 38K

Publishing Venue

Software Patent Institute

Related People

PAUL A. MEDWICK: AUTHOR [+2]

Abstract

Douglas Hartree, who was a mathematical physicist at the University of Manchester and the University of Cambridge during the first half of this century, examined the possibilities for numerical solutions of the many-body problem in quantum mechanics which did not permit analytic, closed-form results. In an attempt to surmount the mathematical complexities associated with multielectron atoms, Hartree proposed the method of self-consistent fields as an approximation scheme which would give numerical forms of atomic wave functions via iterative solution of the Schrodinger equation. Hartree was quick to recognize the need for automatic computation, both analog and digital, for the practical implementation of the technique. To this end, he investigated the application of analog differential analyzers to the problem before realizing the superiority of digital computation. The question of the first self-consistent field calculations to be run on an electronic digital machine is addressed in an effort to clarify misinformation in the existing literature about the use of early computers to perform Hartree computations.

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

Copyright ©; 1988 by the American Federation of Information Processing Societies, Inc. Used with permission.

Douglas Hartree and Early Compulations in Quantum Mechanics

PAUL A. MEDWICK

(Image Omitted: Author's Address: School of Applied and Engineering Physics, Cornell University, Clark Hall, Ithaca, NY 14853- 2501.)

Douglas Hartree, who was a mathematical physicist at the University of Manchester and the University of Cambridge during the first half of this century, examined the possibilities for numerical solutions of the many-body problem in quantum mechanics which did not permit analytic, closed-form results. In an attempt to surmount the mathematical complexities associated with multielectron atoms, Hartree proposed the method of self-consistent fields as an approximation scheme which would give numerical forms of atomic wave functions via iterative solution of the Schrodinger equation. Hartree was quick to recognize the need for automatic computation, both analog and digital, for the practical implementation of the technique. To this end, he investigated the application of analog differential analyzers to the problem before realizing the superiority of digital computation. The question of the first self-consistent field calculations to be run on an electronic digital machine is addressed in an effort to clarify misinformation in the existing literature about the use of early computers to perform Hartree computations.

Categories and Subject Descriptors: K.2 [Computing Milleux]: History of Computing -- people, software. G. 1.8 [Mathematics of Computing]: Numerical Analysis -- partial differential equations. J.2 [Computer Applications]: Physical Sciences and Engineering -- physics. General Terms: Algorithms, Theory. Additional Terms: EDSAC, Hartree, Wave Mechanics, Quantum Mechanics.

Introduction

The introduction of quantum mechanics in the first decades of the 20th century opened up a new realm for thought and discovery in physics. Previously, physicists could conceptualize and experiment with systems which they could touch, see, or otherwise sense directly. It was disconcerting to many that the new theory required the abandonment of predictions based on direct observation of quantum systems, objects of atomic or subatomic dimensions. It became apparent early in the history of the theory that, while indirect observation of such systems through experiment was allowed to some extent, from that time forward physicists would have to become more reliant on pure mathematical analysis to describe and understand the atomic realm.

Many new forms of analytical methods such as Schrodinger's wave mechanics and Heisenberg's matrix mechanics were developed as part of the overall quantum theory. The one which will be addressed here in relation to Hartree's work is wave mechanics. This theory gave analytical results describing many quantum systems, most notably hydrogen and other...