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WALTER KOHN
I suppose
I am not the first Nobelist who, on the occasion of receiving this
Prize, wonders how on earth, by what strange alchemy of family
background, teachers, friends, talents and especially accidents of
history and of personal life he or she arrived at this point. I have
browsed in previous volumes of "Les Prix Nobel" and I know that
there are others whose eventual destinies were foreshadowed early in
their lives – mathematical precocity, champion bird watching,
insatiable reading, mechanical genius. Not in my case, at least not
before my late teens. On the contrary: An early photo of my older
sister and myself, taken at a children's costume party in Vienna – I
look about 7 years old – shows me dressed up in a dark suit and a
black top hat, toy glasses pushed down my nose, and carrying a large
sign under my arm with the inscription "Professor Know-Nothing".
Here then is my attempt to convey to the reader how, at age
75, I see my life which brought me to the present point: a
long-retired professor of theoretical physics at the University of
California, still loving and doing physics, including chemical
physics, mostly together with young people less than half my age;
moderately involved in the life of my community of Santa Barbara and
in broader political and social issues; with unremarkable hobbies
such as listening to classical music, reading (including French
literature), walking with my wife Mara or alone, a little cooking
(unjustifiably proud of my ratatouille); and a weekly half hour of
relaxed roller blading along the shore, a throwback to the
ice-skating of my Viennese childhood. My three daughters and three
grandchildren all live in California and so we get to see each other
reasonably often.
I was naturalized as an American citizen
in 1957 and this has been my primary self-identity ever since. But,
like many other scientists, I also have a strong sense of global
citizenship, including especially Canada, Denmark, England, France
and Israel, where I have worked and lived with a family for
considerable periods, and where I have some of my closest
friends.
My feelings towards Austria, my native land, are –
and will remain – very painful. They are dominated by my vivid
recollections of 1 1/2 years as a Jewish boy under the Austrian Nazi
regime, and by the subsequent murder of my parents, Salomon and
Gittel Kohn, of other relatives and several teachers, during the
holocaust. At the same time I have in recent years been glad to work
with Austrians, one or two generations younger than I: Physicists,
some teachers at my former High School and young people
(Gedenkdiener) who face the dark years of Austria's past honestly
and constructively.
On another level, I want to mention that
I have a strong Jewish identity and – over the years – have been
involved in several Jewish projects, such as the establishment of a
strong program of Judaic Studies at the University of California in San
Diego.
My father, who had lost a brother, fighting on
the Austrian side in World War I, was a committed pacifist. However,
while the Nazi barbarians and their collaborators threatened the
entire world, I could not accept his philosophy and, after several
earlier attempts, was finally accepted into the Canadian Infantry
Corps during the last year of World War II. Many decades later I
became active in attempts to bring an end to the US-Soviet nuclear
arms race and became a leader of unsuccessful faculty initiatives to
terminate the role of the University of California as manager of the
nuclear weapons laboratories at Los Alamos and Livermore. I offered
early support to Jeffrey Leiffer, the founder of the student Pugwash
movement which concerns itself with global issues having a strong
scientific component and in which scientists can play a useful role.
Twenty years after its founding this organization continues strong
and vibrant. My commitment to a humane and peaceful world continues
to this day. I have just joined the Board of the Population
Institute because I am convinced that early stabilization of the
world's population is important for the attainment of this
objective.
After these introductory general reflections from
my present vantage point I would now like to give an idea of my
childhood and adolescence. I was born in 1923 into a middle class
Jewish family in Vienna, a few years after the end of World War I,
which was disastrous from the Austrian point of view. Both my
parents were born in parts of the former Austro-Hungarian Empire, my
father in Hodonin, Moravia, my mother in Brody, then in Galicia,
Poland, now in the Ukraine. Later they both moved to the capital of
Vienna along with their parents. I have no recollection of my
father's parents, who died relatively young. My maternal
grandparents Rappaport were orthodox Jews who lived a simple life of
retirement and, in the case of my grandfather, of prayer and the
study of religious texts in a small nearby synagogue, a Schul as it
was called. My father carried on a business, Postkartenverlag
Brueder Kohn Wien I, whose main product was high quality art
postcards, mostly based on paintings by contemporary artists which
were commissioned by his firm. The business had flourished in the
first two decades of the century but then, in part due to the death
of his brother Adolf in World War I, to the dismantlement of the
Austrian monarchy and to a worldwide economic depression, it
gradually fell on hard times in the 1920s and 1930s. My father
struggled from crisis to crisis to keep the business going and to
support the family. Left over from the prosperous times was a
wonderful summer property in Heringsdorf at the Baltic Sea, not far
from Berlin, where my mother, sister and I spent our summer
vacations until Hitler came to power in Germany in 1933. My father
came for occasional visits (The firm had a branch in Berlin). My
mother was a highly educated woman with a good knowledge of German,
Latin, Polish and French and some acquaintance with Greek, Hebrew
and English. I believe that she had completed an academically
oriented High School in Galicia. Through her parents we maintained
contact with traditional Judaism. At the same time my parents,
especially my father, also were a part of the secular artistic and
intellectual life of Vienna.
After I had completed a public
elementary school, my mother enrolled me in the Akademische
Gymnasium, a fine public high school in Vienna's inner city. There,
for almost five years, I received an excellent education, strongly
oriented toward Latin and Greek, until March 1938, when Hitler
Germany annexed Austria. (This so-called Anschluss was, after a few
weeks, supported by the great majority of the Austrian population).
Until that time my favorite subject had been Latin, whose
architecture and succinctness I loved. By contrast, I had no
interest in, nor apparent talent for, mathematics which was
routinely taught and gave me the only C in high school. During this
time it was my tacit understanding that I would eventually be asked
to take over the family business, a prospect which I faced with
resignation and without the least enthusiasm.
The Anschluss
changed everything: The family business was confiscated but my
father was required to continue its management without any
compensation; my sister managed to emigrate rather promptly to
England; and I was expelled from my school.
In the following
fall I was able to enter a Jewish school, the Chajes Gymnasium,
where I had two extraordinary teachers: In physics, Dr. Emil Nohel,
and in mathematics Dr. Victor Sabbath. While outside the school
walls arbitrary acts of persecution and brutality took place, on the
inside these two inspired teachers conveyed to us their own deep
understanding and love of their subjects. I take this occasion to
record my profound gratitude for their inspiration to which I owe my
initial interest in science. (Alas, they both became victims of Nazi
barbarism).
I note with deep gratitude that twice, during
the Second World War, after having been separated from my parents
who were unable to leave Austria, I was taken into the homes of two
wonderful families who had never seen me before: Charles and Eva
Hauff in Sussex, England, who also welcomed my older sister, Minna.
Charles, like my father, was in art publishing and they had a
business relationship. A few years later, Dr. Bruno Mendel and his
wife Hertha of Toronto, Canada, took me and my friend Joseph
Eisinger into their family. (They also supported three other young
Nazi refugees). Both of these families strongly encouraged me in my
studies, the Hauffs at the East Grinstead County School in Sussex
and the Mendels at the University
of Toronto. I cannot imagine how I might have become a scientist
without their help.
My first wife, Lois Kohn, gave me
invaluable support during the early phases of my scientific career;
my present wife of over 20 years, Mara, has supported me in the
latter phases of my scientific life. She also created a wonderful
home for us, and gave me an entire new family, including her father
Vishniac, a biologist as well as a noted photographer of pre-war
Jewish communities in Eastern Europe, and her mother Luta. (They
both died rather recently, well into their nineties).
After
these rather personal reminiscences I now turn to a brief
description of my life as a scientist.
When I arrived in
England in August 1939, three weeks before the outbreak of World War
II, I had my mind set on becoming a farmer ( I had seen too many
unemployed intellectuals during the 1930s), and I started out on a
training arm in Kent. However, I became seriously ill and physically
weak with meningitis, and so in January 1940 my "acting parents",
the Hauffs, arranged for me to attend the above-mentioned county
school, where – after a period of uncertainty – I concentrated on
mathematics, physics and chemistry.
However, in May 1940,
shortly after I had turned 17, and while the German army swept
through Western Europe and Britain girded for a possible German
air-assault, Churchill ordered most male "enemy aliens" (i.e.,
holders of enemy passports, like myself) to be interned ("Collar the
lot" was his crisp order). I spent about two months in various
British camps, including the Isle of Man, where my school sent me
the books I needed to study. There I also audited, with little
comprehension, some lectures on mathematics and physics, offered by
mature interned scientists.
In July 1940, I was shipped on,
as part of a British convoy moving through U-boat-infested waters,
to Quebec City in Canada; and from there, by train, to a camp in
Trois Rivieres, which housed both German civilian internees and
refugees like myself. Again various internee-taught courses were
offered. The one which interested me most was a course on set-theory
given by the mathematician Dr. Fritz Rothberger and attended by two
students. Dr. Rothberger, from Vienna, a most kind and unassuming
man, had been an advanced private scholar in Cambridge, England, when the
internment order was issued. His love for the intrinsic depth and
beauty of mathematics was gradually absorbed by his
students.
Later I was moved around among various other camps
in Quebec and New Brunswick. Another fellow internee, Dr. A.
Heckscher, an art historian, organized a fine camp school for young
people like myself, whose education had been interrupted and who
prepared to take official Canadian High School exams. In this way I
passed the McGill University
junior Matriculation exam and exams in mathematics, physics and
chemistry on the senior matriculation level. At this point, at age
18, I was pretty firmly looking forward to a career in physics, with
a strong secondary interest in mathematics.
I mention with
gratitude that camp educational programs received support from the
Canadian Red
Cross and Jewish Canadian philanthropic sources. I also mention
that in most camps we had the opportunity to work as lumberjacks and
earn 20 cents per day. With this princely sum, carefully saved up, I
was able to buy Hardy's Pure Mathematics and Slater's Chemical
Physics, books which are still on my shelves. In January 1942,
having been cleared by Scotland Yard of being a potential spy, I was
released from internment and welcomed by the family of Professor
Bruno Mendel in Toronto. At this point I planned to take up
engineering rather than physics, in order to be able to support my
parents after the war. The Mendels introduced me to Professor
Leopold Infeld who had come to Toronto after several years with Einstein.
Infeld, after talking with me (in a kind of drawing room oral exam),
concluded that my real love was physics and advised me to major in
an excellent, very stiff program, then called mathematics and
physics, at the University of Toronto. He argued that this program
would enable me to earn a decent living at least as well as an
engineering program.
However, because of my now German
nationality, I was not allowed into the chemistry building, where
war work was in progress, and hence I could not enroll in any
chemistry courses. (In fact, the last time I attended a chemistry
class was in my English school at the age of 17.) Since chemistry
was required, this seemed to sink any hope of enrolling. Here I
express my deep appreciation to Dean and head of mathematics, Samuel
Beatty, who helped me, and several others, nevertheless to enter
mathematics and physics as special students, whose status was
regularized one or two years later.
I was fortunate to find
an extraordinary mathematics and applied mathematics program in
Toronto. Luminous members whom I recall with special vividness were
the algebraist Richard Brauer, the non-Euclidean geometer, H.S.M.
Coxeter, the aforementioned Leopold Infeld, and the classical
applied mathematicians John Lighton Synge and Alexander Weinstein.
This group had been largely assembled by Dean Beatty. In those years
the University of Toronto team of mathematics students, competing
with teams from the leading North-American Institutions,
consistently won the annual Putman competition. (For the record I
remark that I never participated). Physics too had many
distinguished faculty members, largely recruited by John C.
McLennan, one of the earliest low temperature physicists, who had
died before I arrived. They included the Raman
specialist H.L. Welsh, M.F. Crawford in optics and the
low-temperature physicists H.G. Smith and A.D. Misener. Among my
fellow students was Arthur
Schawlow, who later was to share the Nobel Prize for the
development of the laser.
During one or two summers, as well
as part-time during the school year, I worked for a small Canadian
company which developed electrical instruments for military planes.
A little later I spent two summers, working for a geophysicist,
looking for (and finding!) gold deposits in northern Ontario and
Quebec.
After my junior year I joined the Canadian Army. An
excellent upper division course in mechanics by A. Weinstein had
introduced me to the dynamics of tops and gyroscopes. While in the
army I used my spare time to develop new strict bounds on the
precession of heavy, symmetrical tops. This paper, "Contour
Integration in the Theory of the Spherical Pendulum and the Heavy
Symmetrical Top" was published in the Transactions of American
Mathematical Society. At the end of one year's army service, having
completed only 2 1/2 out of the 4-year undergraduate program, I
received a war-time bachelor's degree "on – active – service" in
applied mathematics.
In the year 1945-6, after my discharge
from the army, I took an excellent crash master's program, including
some of the senior courses which I had missed, graduate courses, a
master's thesis consisting of my paper on tops and a paper on
scaling of atomic wave-functions.
My teachers wisely
insisted that I do not stay on in Toronto for a Ph.D, but financial
support for further study was very hard to come by. Eventually I was
thrilled to receive a fine Lehman fellowship at Harvard. Leopold Infeld
recommended that I should try to be accepted by Julian
Schwinger, whom he knew and who, still in his 20s, was already
one of the most exciting theoretical physicists in the world.
Arriving from the relatively isolated University of Toronto
and finding myself at the illustrious Harvard, where many faculty
and graduate students had just come back from doing brilliant
war-related work at Los Alamos, the
MIT Radiation Laboratory, etc., I felt very insecure and set as
my goal survival for at least one year. The Department Chair, J. H.
Van Vleck, was very kind and referred to me as the Toronto-Kohn
to distinguish me from another person who, I gathered, had caused
some trouble. Once Van Vleck told me of an idea in the band-theory
of solids, later known as the quantum defect method, and asked me if
I would like to work on it. I asked for time to consider. When I
returned a few days later, without in the least grasping his idea, I
thanked him for the opportunity but explained that, while I did not
yet know in what subfield of physics I wanted to do my thesis, I was
sure it would not be in solid state physics. This problem then
became the thesis of Thomas Kuhn, (later a renowned philosopher of
science), and was further developed by myself and others. In spite
of my original disconnect with Van Vleck, solid state physics soon
became the center of my professional life and Van Vleck and I became
lifelong friends.
After my encounter with Van Vleck I
presented myself to Julian Schwinger requesting to be accepted as
one of his thesis students. His evident brilliance as a researcher
and as a lecturer in advanced graduate courses (such as waveguides
and nuclear physics) attracted large numbers of students, including
many who had returned to their studies after spending "time out" on
various war-related projects.
I told Schwinger briefly of my
very modest efforts using variational principles. He himself had
developed brilliant new Green's function variational principles
during the war for wave-guides, optics and nuclear physics (Soon
afterwards Green's functions played an important role in his
Nobel-Prize-winning work on quantum electrodynamics). He accepted me
within minutes as one of his approximately 10 thesis students. He
suggested that I should try to develop a Green's function
variational method for three-body scattering problems, like
low-energy neutron-deuteron scattering, while warning me ominously,
that he himself had tried and failed. Some six months later, when I
had obtained some partial, very unsatisfactory results, I looked for
alternative approaches and soon found a rather elementary
formulation, later known as Kohn's variational principle for
scattering, and useful for nuclear, atomic and molecular problems.
Since I had circumvented Schwinger's beloved Green's functions, I
felt that he was very disappointed. Nevertheless he accepted this
work as my thesis in 1948. (Much later L. Fadeev offered his
celebrated solution of the three-body scattering problem).
My Harvard friends, close and not so close, included P.W.
Anderson, N.
Bloembergen, H. Broida (a little later), K. Case, F. De Hoffman,
J. Eisenstein, R. Glauber, T. Kuhn, R. Landauer, B.
Mottelson, G. Pake, F. Rohrlich, and C. Slichter. Schwinger's
brilliant lectures on nuclear physics also attracted many students
and Postdocs from MIT, including J. Blatt, M. Goldberger, and J. M.
Luttinger. Quite a number of this remarkable group would become
lifelong friends, and one – J. M. "Quin" Luttinger – also my closest
collaborators for 13 years, 1954-66. Almost all went on to
outstanding careers of one sort or another.
I was totally
surprised and thrilled when in the spring of 1948 Schwinger offered
to keep me at Harvard for up to three years. I had the choice of
being a regular post-doctoral fellow or dividing my time equally
between research and teaching. Wisely – as it turned out – I chose
the latter. For the next two years I shared an office with Sidney
Borowitz, later Chancellor of New York
University, who had a similar appointment. We were to assist
Schwinger in his work on quantum electrodynamics and the emerging
field theory of strong interactions between nucleons and mesons. In
view of Schwinger's deep physical insights and celebrated
mathematical power, I soon felt almost completely useless. Borowitz
and I did make some very minor contributions, while the greats,
especially Schwinger and Feynman,
seemed to be on their way to unplumbed, perhaps ultimate depths.
For the summer of 1949, 1 got a job in the Polaroid
laboratory in Cambridge, Mass., just before the Polaroid camera made
its public appearance. My task was to bring some understanding to
the mechanism by which charged particles falling on a photographic
plate lead to a photographic image. (This technique had just been
introduced to study cosmic rays). I therefore needed to learn
something about solid state physics and occasionally, when I
encountered things I didn't understand, I consulted Van Vleck.
It seems that these meetings gave him the erroneous
impression that I knew something about the subject. For one day he
explained to me that he was about to take a leave of absence and,
"since you are familiar with solid state physics", he asked me if I
could teach a course on this subject, which he had planned to offer.
This time, frustrated with my work on quantum field theory, I
agreed. I had a family, jobs were scarce, and I thought that
broadening my competence into a new, more practical, area might give
me more opportunities.
So, relying largely on the excellent,
relatively recent monograph by F. Seitz, "Modern Theory Of Solids",
I taught one of the first broad courses on Solid State Physics in
the United States. My "students" included several of my friends, N.
Bloembergen, C. Slichter and G. Pake who conducted experiments
(later considered as classics) in the brand-new area of nuclear
magnetic resonance which had just been opened up by E.
Purcell at Harvard and F.
Bloch at Stanford. Some of my students often understood much
more than I, they were charitable towards their teacher.
At
about the same time I did some calculations suggested by
Bloembergen, on the recently discovered, so-called Knight shift of
nuclear magnetic resonance, and, in this connection, returning to my
old love of variational methods, developed a new variational
approach to the study of wavefunctions in periodic
crystals.
Although my appointment was good for another year
and a half, I began actively looking for a more long-term position.
I was a naturalized Canadian citizen, with the warmest feelings
towards Canada, and explored every Canadian university known to me.
No opportunities presented themselves. Neither did the very meager
US market for young theorists yield an academic offer. At this point
a promising possibility appeared for a position in a new
Westinghouse nuclear reactor laboratory outside of Pittsburgh. But
during a visit it turned out that US citizenship was required and so
this possibility too vanished. At that moment I was unbelievably
lucky. While in Pittsburgh, I stayed with my Canadian friend Alfred
Schild, who taught in the mathematics department at the Carnegie
Institute of Technology (now Carnegie
Mellon University). He remarked that F. Seitz and several of his
colleagus had just left the physics department and moved to
Illinois, so that – he thought – there might be an opening for me
there. It turned out that the Department Chair, Ed Creutz was
looking rather desperately for somebody who could teach a course in
solid state physics and also keep an eye on the graduate students
who had lost their "doctor-fathers". Within 48 hours I had a
telegram offering me a job!
A few weeks later a happy
complication arose. I had earlier applied for a National Research
Council fellowship for 1950-51 and now it came through. A request
for a short postponement was firmly denied. Fortunately, Ed Creutz
agreed to give me a one-year leave of absence, provided I first
taught a compressed course in solid state physics. So on December
31, 1950 (to satisfy the terms of my fellowship) I arrived in
Copenhagen.
Originally I had planned to revert to nuclear
physics there, in particular the the structure of the deuteron. But
in the meantime I had become a solid state physicist. Unfortunately
no one in Copenhagen, including Niels
Bohr, had even heard the expression "Solid State Physics". For a
while I worked on old projects. Then, with an Indian visitor named
Vachaspati (no initial), I published a criticism of Froehlich's
pre-BCS theory of superconductivity, and also did some work on
scattering theory.
In the spring of 1951, I was told that an
expected visitor for the coming year had dropped out and that the
Bohr Institute could provide me with an Oersted fellowship to remain
there until the fall of 1952. Very exciting work was going on in
Copenhagen, which eventually led to the great "Collective Model of
the Nucleus" of A. Bohr and B. Mottelson, both of whom had become
close friends. Furthermore my family and I had fallen in love with
Denmark and the Danish people. A letter from Niels Bohr to my
department chair at Carnegie quickly resulted in the extension of my
leave of absence till the fall of 1952.
In the summer of
1951, I became a substitute teacher, replacing an ill lecturer at
the first summer school at Les Houches, near Chamonix in France,
conceived and organized by a dynamic young French woman, Cécile
Morette De Witt. As an "expert" in solid state physics, I offered a
few lectures on that subject. Wolfgang
Pauli, who visited, when he learned of my meager knowledge of
solids, mostly metallic sodium, asked me, true to form, if I was a
professor of physics or of sodium. He was equally acerbic about
himself. Some 50 years old at the time, he described himself as "a
child-wonder in menopause" ("ein Wunderkind in den Wechseljahren").
But my most important encounter was with Res Jost, an assistant of
Pauli at the ETH in Zurich, with whom I shared an interest in the
so-called inverse scattering problem: given asymptotic information,
(such as phase-shifts as function of energy), of a particle
scattered by a potential V(r), what quantitative information can be
inferred about this potential? Later that year, we both found
ourselves in Copenhagen and addressed this problem in earnest. Jost,
at the time a senior fellow at the Institute for Advanced Study in
Princeton, had to return
there before we had finished our work. A few months later, in the
spring of 1952, I received an invitation from Robert Oppenheimer, to
come to Princeton for a few weeks to finish our project. In an
intensive and most enjoyable collaboration, we succeeded in
obtaining a complete solution for S-wave scattering by a spherical
potential. At about the same time I.M. Gel'fand in the Soviet Union
published his celebrated work on the inverse problem. Jost and I
remained close lifelong friends until his death in 1989.
After my return to Carnegie Tech in 1952, I began a major
collaboration with N. Rostoker, then an assistant of an
experimentalist, later a distinguished plasma theorist. We developed
a theory for the energy band structure of electrons for periodic
potentials, harking back to my earlier experience with scattering,
Green's functions and variational methods. We showed how to
determine the bandstructure from a knowledge of purely geometric
structure constants and a small number (~ 3) of scattering
phase-shifts of the potential in a single sphericalized cell. By a
different approach this theory was also obtained by J. Korringa. It
continues to be used under the acronym KKR. Other work during my
Carnegie years, 1950-59, includes the image of the metallic Fermi
Surface in the phonon spectrum (Kohn anomaly); exponential
localization of Wannier functions; and the nature of the insulating
state.
My most distinguished colleague and good friend at
Carnegie was G.C. Wick, and my first PhD's were D. Schechter and V.
Ambegaokar. I also greatly benefitted from my interaction with T.
Holstein at Westinghouse.
In 1953, with support from Van
Vleck, I obtained a summerjob at Bell Labs as assistant of W.
Shockley, the co-inventor of the transistor. My project was
radiation damage of Si and Ge by energetic electrons, critical for
the use of the recently developed semiconductor devices for
applications in outer space. In particular, I established a
reasonably accurate energy threshold for permanent displacement of a
nucleus from its regular lattice position, substantially smaller
than had been previously presumed. Bell Labs at that time was
without question the world's outstanding center for research in
solid state physics and for the first time, gave me a perspective
over this fascinating, rich field. Bardeen,
Brattain
and Shockley , after their invention of the transistor, were the
great heroes. Other world class theorists were C. Herring, G.
Wannier and my brilliant friend from Harvard, P.W. Anderson. With a
few interruptions I was to return to Bell Labs every year until
1966. I owe this institution my growing up from amateur to
professional.
In the summer of 1954 both Quin Luttinger and
I were at Bell Labs and began our 13-year long collaborations, along
with other work outside our professional "marriage". (Our close
friendship lasted till his death in 1997). The all-important
impurity states in the transistor materials Si and Ge, which govern
their electrical and many of their optical properties, were under
intense experimental study, which we complemented by theoretical
work using so-called effective mass theory. In 1957, 1 wrote a
comprehensive review on this subject. We (mostly Luttinger) also
developed an effective Hamiltonian in the presence of magnetic
fields, for the complex holes in these elements. A little later we
obtained the first non-heuristic derivation of the Boltzman
transport equation for quantum mechanical particles. There
followed several years of studies of many-body theories, including
Luttinger's famous one-dimensional "Luttinger liquid" and the
"Luttinger's theorem" about the conservation of the volume enclosed
by a metallic Fermi surface, in the presence of electron electron
interaction. Finally, in 1966, we showed that superconductivity
occurs even with purely repulsive interactions – contrary to
conventional wisdom and possibly relevant to the much later
discovery of high-Tc superconductors.
In 1960, when I moved
to the University of California San Diego, California, my scientific
interactions with Luttinger, then at Columbia University, and with
Bell Labs gradually diminished. I did some consulting at the nearby
General Atomic Laboratory, interacting primarily with J. Appel. My
university colleagues included G. Feher, B. Maple, B. Matthias, S.
Schultz, H. Suhl and J. Wheatley, – a wonderful environment. During
my 19-year stay there I typically worked with two postdocs and four
graduate students. A high water mark period were the late 1960s,
early 1970s, including N. Lang, D. Mermin, M. Rice, L. J. Sham, D.
Sherrington, and J. Smith.
I now come to the development of
density functional theory (DFT). In the fall of 1963, I spent a
sabbatical semester at the École Normale Supérieure in Paris, as
guest and in the spacious office of my friend Philippe Nozières.
Since my Carnegie days I had been interested in the electronic
structure of alloys, a subject of intense experimental interest in
both the physics and metallurgy departments. In Paris I read some of
the metallurgical literature, in which the concept of the effective
charge e* of an atom in an alloy was prominent, which characterized
in a rough way the transfer of charge between atomic cells. It was a
local point of view in coordinate space, in contrast
to the emphasis on delocalized waves in momentum
space, such as Bloch-waves in an average periodic crystal, used
for the rough description of substitutional alloys. At this point
the question occurred to me whether, in general, an alloy is
completely or only partially characterized by its electronic
density distribution n(r): In the back of my mind I knew that this
was the case in the Thomas-Fermi approximation of interacting
electron systems; also, from the "rigid band model" of
substitutional alloys of neighboring elements, I knew that there was
a 1-to-1 correspondence between a weak perturbing potential
v(r) and the corresponding small change n(r) of the
density distribution. Finally it occurred to me that for a single
particle there is an explicit elementary relation between the
potential v(r) and the density, n(r), of the groundstate. Taken
together, these provided strong support for the conjective that the
density n(r) completely determines the external potential v(r). This
would imply that n(r) which integrates to N, the total number of
electrons, also determines the total Hamilton H and hence all
properties derivable from H and N, e.g. the wavefunction of the 17th
excited state, 17 (r1,...,rN)!
Could this be true? And how could it be decided? Could two different
potentials, v1(r) and v2(r), with associated
different groundstates 1
(r1,...,rN) and 2
(r1,...,rN) give rise to the same
density distribution? It turned out that a simple 3-line argument,
using my beloved Rayleigh Ritz variational principle, confirmed the
conjecture. It seemed such a remarkable result that I did not trust
myself.
By this time I had become friends with another
inhabitant of Nozière's office, Pierre Hohenberg, a lively young
American, recently arrived in Paris after a one-year fellowship in
the Soviet Union. Having completed some work there he seemed to be
"between" problems and I asked if he would be interested in joining
me. He was. The first task was a literature search to see if this
simple result was already known; apparently not. In short order we
had recast the Rayleigh-Ritz variational theorem for the groundstate
energy in terms of the density n (r) instead of the many electron
wave function , leading to what is now called the Hohenberg Kohn
(HK) variational principle. We fleshed out this work with various
approximations and published it.
Shortly afterwards I
returned to San Diego where my new postdoctoral fellow, Lu J. Sham
had already arrived. Together we derived from the HK variational
principle what are now known as the Kohn-Sham (KS) equations, which
have found extensive use by physicists and chemists, including
members of my group.
Since the 1970s I have also been working
on the theory of surfaces, mostly electronic structure. The work
with Lang in the early 1970s, using DFT, picked up and carried
forward where J. Bardeen's thesis had left off in the
1930s.
In 1979, I moved to the University of California,
Santa Barbara to become the initial director of the National Science
Foundation's Institute for Theoretical Physics (1979-84). I have
continued to work with postdoctoral fellows and students on DFT and
other problems that I had put aside in previous years. Since the
middle 1980s, I have also had increasing, fruitful interactions with
theoretical chemists. I mention especially Robert Parr, the first
major theoretical chemist to believe in the potential promise of DFT
for chemistry who, together with his young co-workers, has made
major contributions, both conceptual and computational.
Since beginning this autobiographical sketch I have turned
76. I enormously enjoy the continuing progress by my younger DFT
colleagues and my own collaboration with some of them. Looking back
I feel very fortunate to have had a small part in the great drama of
scientific progress, and most thankful to all those, including
family, kindly "acting parents", teachers, colleagues, students, and
collaborators of all ages, who made it possible.
From Les
Prix Nobel 1998. |
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