Douglas Hartree
Encyclopedia
Douglas Rayner Hartree PhD
, FRS (27 March 1897 – 12 February 1958) was an English
mathematician
and physicist
most famous for the development of numerical analysis
and its application to the Hartree-Fock equations of atomic physics
and the construction of the meccano
differential analyser
.
, United Kingdom
. His father, William, was a lecturer in engineering
at Cambridge University
and his mother, Eva Rayner, was president of the National Council of Women and mayor of the city of Cambridge. One of his great-grandfathers was Samuel Smiles
; another was the marine engineer William Hartree, partner of John Penn
.
He was the oldest of three sons, although his two younger brothers did not survive to adulthood. He attended St John's College, Cambridge
but the first world war
interrupted his studies. He joined a group working on anti-aircraft ballistics
under A. V. Hill, where he gained considerable skill and an abiding interest in practical calculation and numerical methods for differential equations, executing most of his own work with pencil and paper.
After the end of World War I, Hartree returned to Cambridge graduating in 1922 with a Second Class degree in natural sciences.
to Cambridge inspired Douglas to apply his numerical skills to Bohr’s theory
of the atom for which he obtained his Ph.D.
in 1926. With the publication of Schrödinger’s equation
in the same year, Douglas was able to apply his knowledge
of differential equations and numerical analysis
to the new quantum theory
.
He derived the Hartree equations for the distribution of electrons in an atom and proposed the self-consistent field method for their solution. The wavefunctions from this theory did not satisfy the Pauli exclusion principle
for which Slater
showed that determinantal functions are required. V. Fock
published the ``equations with exchange’’ now known as Hartree-Fock equations. These are considerably more demanding computationally even with the efficient methods Hartree proposed for the calculation of exchange contributions.
at the University of Manchester
. In 1933, he visited Vannevar Bush
at the Massachusetts Institute of Technology
and learned at first hand about his differential analyser
. Immediately on his return to Manchester
, he set about building his own analyser from Meccano
. Seeing the potential for further exploiting his numerical methods using the machine he prevailed on Sir Robert McDougall to fund a more robust machine which was built in collaboration with Metropolitan-Vickers
.
The first application of the machine reflected Hartree's enthusiasm for railways
in calculating timetables for the London, Midland and Scottish Railway
.
He spent the rest of the decade applying the differential analyzer to the solution of differential equations arising in physics. These included control theory and laminar boundary layer theory in fluid dynamics making significant contributions to each of the fields.
The differential analyzer was not suitable for the solution of equations with exchange. When Fock’s
publication pre-empted Hartree’s work on equations with exchange, Hartree turned his research to radio-wave propagation that led to the Appleton-Hartree equation
. In 1935, his father, William Hartree, offered to do calculations for him. Results with exchange soon followed. Douglas recognized the importance of configuration interaction
that he referred to as "superposition of configurations".
The first multiconfiguration Hartree-Fock results were published by father, son, and Bertha Swirles
(later Lady Jeffreys) in 1939.
At Hartree’s suggestion, Bertha Swirles proceeded to derive equations with exchange for atoms using the Dirac equation
in 1935. With Hartree’s advice, the first relativistic calculations (without exchange) were reported in 1940 by A. O. Williams, a student of R. B. Lindsay
.
, Hartree supervised two computing groups. The first group, for the Ministry of Supply, has been described by Jack Howlett
as a ‘`job shop’’ for the solution of differential equations. At the outbreak of World War II, the differential analyzer at the University
of Manchester was the only full-size (8 integrator)
differential analyzer in the country. Arrangements were made to have the machine available
for work in support of the national war effort. In time, the group consisted of four members
(front to back: Jack Howlett, Nicholas R. Eyres, J. G. L. Michel; center, Douglas Hartree; right Phyllis Lockett Nicolson). Problems were submitted to the group without information about the source but included the automatic tracking of targets, radio propagation, underwater explosions, heat flow in steel, and the diffusion equation later found to be for isotope separation. The second group was the magnetron research group of
Phyllis Lockett Nicolson
, David Copely, and Oscar Buneman
.
The work was done for the Committee for the Co-ordination of the Valve Development assisting the development of radar. A differential analyzer could have been used if more integrators had been available, so Hartree set up his group as three "CPUs" to work on mechanical desk calculators in parallel. For a method of solution he selected what is now a classical particle simulation.
Hartree never published any of his magnetron research findings in journals though he wrote numerous highly technical secret reports during the war.
s and was involved in the early application of digital computers, advising the U.S.
military on the use of ENIAC
for calculating ballistics tables. In 1946 he was the first civilian to program the ENIAC
as an evaluation of its applicability to a broad range of science. For this he selected a problem involving the flow of a compressible fluid over a surface such as air over the surface of a wing travelling faster than the speed of sound.
Hartree's last Ph.D. student at Cambridge, Charlotte Froese Fischer
, would become world-famous for the development and implementation of the multi-configuration Hartree–Fock (MCHF) approach to atomic structure calculations and for her theoretical prediction concerning the existence of the negative calcium ion.
He died of heart failure in Addenbrooke's Hospital
, Cambridge in Feb. 12, 1958.
PHD
PHD may refer to:*Ph.D., a doctorate of philosophy*Ph.D. , a 1980s British group*PHD finger, a protein sequence*PHD Mountain Software, an outdoor clothing and equipment company*PhD Docbook renderer, an XML renderer...
, FRS (27 March 1897 – 12 February 1958) was an English
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
most famous for the development of numerical analysis
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
and its application to the Hartree-Fock equations of atomic physics
Atomic physics
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and...
and the construction of the meccano
Meccano
Meccano is a model construction system comprising re-usable metal strips, plates, angle girders, wheels, axles and gears, with nuts and bolts to connect the pieces. It enables the building of working models and mechanical devices....
differential analyser
Differential analyser
The differential analyser is a mechanical analogue computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration...
.
Early life
Douglas Hartree was born in CambridgeCambridge
The city of Cambridge is a university town and the administrative centre of the county of Cambridgeshire, England. It lies in East Anglia about north of London. Cambridge is at the heart of the high-technology centre known as Silicon Fen – a play on Silicon Valley and the fens surrounding the...
, United Kingdom
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
. His father, William, was a lecturer in engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
at Cambridge University
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
and his mother, Eva Rayner, was president of the National Council of Women and mayor of the city of Cambridge. One of his great-grandfathers was Samuel Smiles
Samuel Smiles
-Early life:Born in Haddington, East Lothian, Scotland, the son of Samuel Smiles of Haddington and Janet Wilson of Dalkeith, Smiles was one of eleven surviving children. The family were strict Cameronians, though when Smiles grew up he was not one of them...
; another was the marine engineer William Hartree, partner of John Penn
John Penn (engineer)
John Penn FRS, was a marine engineer, whose firm was pre-eminent in the middle of the nineteenth century due to his innovations in engine and propeller systems, which led his firm to be the major supplier to the Royal Navy as it made the transition from sail to steam power...
.
He was the oldest of three sons, although his two younger brothers did not survive to adulthood. He attended St John's College, Cambridge
St John's College, Cambridge
St John's College is a constituent college of the University of Cambridge. The college's alumni include nine Nobel Prize winners, six Prime Ministers, three archbishops, at least two princes, and three Saints....
but the first world war
World War I
World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...
interrupted his studies. He joined a group working on anti-aircraft ballistics
Ballistics
Ballistics is the science of mechanics that deals with the flight, behavior, and effects of projectiles, especially bullets, gravity bombs, rockets, or the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance.A ballistic body is a body which is...
under A. V. Hill, where he gained considerable skill and an abiding interest in practical calculation and numerical methods for differential equations, executing most of his own work with pencil and paper.
After the end of World War I, Hartree returned to Cambridge graduating in 1922 with a Second Class degree in natural sciences.
Atomic structure calculations
In 1921, a visit by Niels BohrNiels Bohr
Niels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Bohr mentored and collaborated with many of the top physicists of the century at his institute in...
to Cambridge inspired Douglas to apply his numerical skills to Bohr’s theory
Bohr model
In atomic physics, the Bohr model, introduced by Niels Bohr in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with electrostatic forces providing attraction,...
of the atom for which he obtained his Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
in 1926. With the publication of Schrödinger’s equation
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....
in the same year, Douglas was able to apply his knowledge
of differential equations and numerical analysis
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
to the new quantum theory
Introduction to quantum mechanics
Quantum mechanics is the body of scientific principles that explains the behavior of matter and its interactions with energy on the scale of atoms and atomic particles....
.
He derived the Hartree equations for the distribution of electrons in an atom and proposed the self-consistent field method for their solution. The wavefunctions from this theory did not satisfy the Pauli exclusion principle
Pauli exclusion principle
The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is anti-symmetric with respect to exchange of the particles...
for which Slater
John C. Slater
John Clarke Slater was a noted American physicist who made major contributions to the theory of the electronic structure of atoms, molecules and solids. This work is of ongoing importance in chemistry, as well as in many areas of physics. He also made major contributions to microwave electronics....
showed that determinantal functions are required. V. Fock
Vladimir Fock
Vladimir Aleksandrovich Fock was a Soviet physicist, who did foundational work on quantum mechanics and quantum electrodynamics....
published the ``equations with exchange’’ now known as Hartree-Fock equations. These are considerably more demanding computationally even with the efficient methods Hartree proposed for the calculation of exchange contributions.
Manchester years
In 1929, Hartree was appointed to the Beyer Chair of Applied MathematicsBeyer Chair of Applied Mathematics
The Beyer Chair of Applied Mathematics is an endowed professorial position in the School of Mathematics, University of Manchester, England. The endowment came from the engineer Charles Frederick Beyer, a generous supporter of the University....
at the University of Manchester
School of Mathematics, University of Manchester
The School of Mathematics at the University of Manchester is one of the largest mathematics departments in the United Kingdom, with around 80 academic staff and an undergraduate intake of roughly 400 a year and another 200 postgraduate students...
. In 1933, he visited Vannevar Bush
Vannevar Bush
Vannevar Bush was an American engineer and science administrator known for his work on analog computing, his political role in the development of the atomic bomb as a primary organizer of the Manhattan Project, the founding of Raytheon, and the idea of the memex, an adjustable microfilm viewer...
at the Massachusetts Institute of Technology
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
and learned at first hand about his differential analyser
Differential analyser
The differential analyser is a mechanical analogue computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration...
. Immediately on his return to Manchester
Manchester
Manchester is a city and metropolitan borough in Greater Manchester, England. According to the Office for National Statistics, the 2010 mid-year population estimate for Manchester was 498,800. Manchester lies within one of the UK's largest metropolitan areas, the metropolitan county of Greater...
, he set about building his own analyser from Meccano
Meccano
Meccano is a model construction system comprising re-usable metal strips, plates, angle girders, wheels, axles and gears, with nuts and bolts to connect the pieces. It enables the building of working models and mechanical devices....
. Seeing the potential for further exploiting his numerical methods using the machine he prevailed on Sir Robert McDougall to fund a more robust machine which was built in collaboration with Metropolitan-Vickers
Metropolitan-Vickers
Metropolitan-Vickers, Metrovick, or Metrovicks, was a British heavy electrical engineering company of the early-to-mid 20th century formerly known as British Westinghouse. Highly diversified, they were particularly well known for their industrial electrical equipment such as generators, steam...
.
The first application of the machine reflected Hartree's enthusiasm for railways
Rail transport
Rail transport is a means of conveyance of passengers and goods by way of wheeled vehicles running on rail tracks. In contrast to road transport, where vehicles merely run on a prepared surface, rail vehicles are also directionally guided by the tracks they run on...
in calculating timetables for the London, Midland and Scottish Railway
London, Midland and Scottish Railway
The London Midland and Scottish Railway was a British railway company. It was formed on 1 January 1923 under the Railways Act of 1921, which required the grouping of over 120 separate railway companies into just four...
.
He spent the rest of the decade applying the differential analyzer to the solution of differential equations arising in physics. These included control theory and laminar boundary layer theory in fluid dynamics making significant contributions to each of the fields.
The differential analyzer was not suitable for the solution of equations with exchange. When Fock’s
Vladimir Fock
Vladimir Aleksandrovich Fock was a Soviet physicist, who did foundational work on quantum mechanics and quantum electrodynamics....
publication pre-empted Hartree’s work on equations with exchange, Hartree turned his research to radio-wave propagation that led to the Appleton-Hartree equation
Appleton-Hartree equation
The Appleton-Hartree equation, sometimes also referred to as the Appleton-Lassen equation is a mathematical expression that describes the refractive index for electromagnetic wave propagation in a cold magnetized plasma...
. In 1935, his father, William Hartree, offered to do calculations for him. Results with exchange soon followed. Douglas recognized the importance of configuration interaction
Configuration interaction
Configuration interaction is a post-Hartree–Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born–Oppenheimer approximation for a quantum chemical multi-electron system. Mathematically, configuration simply describes the linear combination...
that he referred to as "superposition of configurations".
The first multiconfiguration Hartree-Fock results were published by father, son, and Bertha Swirles
Bertha Swirles
Bertha Swirles, Lady Jeffreys , carried out research on quantum theory, particularly in its early days. She was associated with Girton College, University of Cambridge, as student and Fellow, for over 70 years....
(later Lady Jeffreys) in 1939.
At Hartree’s suggestion, Bertha Swirles proceeded to derive equations with exchange for atoms using the Dirac equation
Dirac equation
The Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928. It provided a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity, and...
in 1935. With Hartree’s advice, the first relativistic calculations (without exchange) were reported in 1940 by A. O. Williams, a student of R. B. Lindsay
Robert Bruce Lindsay
Robert Bruce Lindsay was an American physicist and physics professor, known for his prolific authorship of physics books in acoustics, and historical and philosophical analyses of physics.-Biography:...
.
World War II
During World War IIWorld War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, Hartree supervised two computing groups. The first group, for the Ministry of Supply, has been described by Jack Howlett
Jack Howlett
Jack Howlett was a British mathematician and computer scientist who was head of the Atlas Computer Laboratory for the duration of its existence.- Personal life and early career :...
as a ‘`job shop’’ for the solution of differential equations. At the outbreak of World War II, the differential analyzer at the University
of Manchester was the only full-size (8 integrator)
differential analyzer in the country. Arrangements were made to have the machine available
for work in support of the national war effort. In time, the group consisted of four members
(front to back: Jack Howlett, Nicholas R. Eyres, J. G. L. Michel; center, Douglas Hartree; right Phyllis Lockett Nicolson). Problems were submitted to the group without information about the source but included the automatic tracking of targets, radio propagation, underwater explosions, heat flow in steel, and the diffusion equation later found to be for isotope separation. The second group was the magnetron research group of
Phyllis Lockett Nicolson
Phyllis Nicolson
Phyllis Nicolson was a British mathematician most known for her work on the Crank–Nicolson scheme together with John Crank....
, David Copely, and Oscar Buneman
Oscar Buneman
Oscar Buneman made advances in science, engineering, and mathematics. Buneman was a pioneer of computational plasma physics and plasma simulation....
.
The work was done for the Committee for the Co-ordination of the Valve Development assisting the development of radar. A differential analyzer could have been used if more integrators had been available, so Hartree set up his group as three "CPUs" to work on mechanical desk calculators in parallel. For a method of solution he selected what is now a classical particle simulation.
Hartree never published any of his magnetron research findings in journals though he wrote numerous highly technical secret reports during the war.
Later life and work
Hartree had moved to theoretical physics in 1937 before returning to Cambridge to take up the post of Plummer professor of mathematical physics in 1946. He did further work in control systemControl system
A control system is a device, or set of devices to manage, command, direct or regulate the behavior of other devices or system.There are two common classes of control systems, with many variations and combinations: logic or sequential controls, and feedback or linear controls...
s and was involved in the early application of digital computers, advising the U.S.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
military on the use of ENIAC
ENIAC
ENIAC was the first general-purpose electronic computer. It was a Turing-complete digital computer capable of being reprogrammed to solve a full range of computing problems....
for calculating ballistics tables. In 1946 he was the first civilian to program the ENIAC
ENIAC
ENIAC was the first general-purpose electronic computer. It was a Turing-complete digital computer capable of being reprogrammed to solve a full range of computing problems....
as an evaluation of its applicability to a broad range of science. For this he selected a problem involving the flow of a compressible fluid over a surface such as air over the surface of a wing travelling faster than the speed of sound.
Hartree's last Ph.D. student at Cambridge, Charlotte Froese Fischer
Charlotte Froese Fischer
Acad. Prof. Dr. Charlotte Froese Fischer PhD is a Canadian-American applied mathematician and computer scientist who gained world recognition for the development and implementation of the Multi-configurational Hartree-Fock approach to atomic structure calculations and for her theoretical...
, would become world-famous for the development and implementation of the multi-configuration Hartree–Fock (MCHF) approach to atomic structure calculations and for her theoretical prediction concerning the existence of the negative calcium ion.
He died of heart failure in Addenbrooke's Hospital
Addenbrooke's Hospital
Addenbrooke's Hospital is an internationally renowned teaching hospital in Cambridge, England, with strong links to the University of Cambridge. It was founded in 1766 on Trumpington Street with £4,500 from the will of Dr John Addenbrooke, a fellow of St Catharine's College...
, Cambridge in Feb. 12, 1958.
Honours
- Fellow of the Royal SocietyRoyal SocietyThe Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
, (1932) - The Hartree unit of energyHartree energyThe hartree , also known as the Hartree energy, is the atomic unit of energy, named after the British physicist Douglas Hartree. It is defined as...
is named after him.
See also
- Appleton-Hartree equationAppleton-Hartree equationThe Appleton-Hartree equation, sometimes also referred to as the Appleton-Lassen equation is a mathematical expression that describes the refractive index for electromagnetic wave propagation in a cold magnetized plasma...
- Differential analyzerDifferential analyserThe differential analyser is a mechanical analogue computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration...
- Hartree (unit of energy)
- Hartree equation
- Hartree-Fock method
- Oscar BunemanOscar BunemanOscar Buneman made advances in science, engineering, and mathematics. Buneman was a pioneer of computational plasma physics and plasma simulation....