Hylleraas, Egil Andersen

(b. Engerdal, Norway, 15 May 1898; d. Oslo, Norway, 28 October 1965)

Physics.

Hylleraas (the name is taken from the farm where he was born) was the son of Ole Andersen, a school-teacher, and the former Inger Rømoen. The youngest of eleven children, he grew up in the rural community of Engerdal. Following elementary school he worked for a few years as a logger. In 1918 he entered the University of Christiania (now Oslo), where he studied mathematics and physics. After his graduation in 1924 he worked for two years as a high school teacher in Oslo. Articles on double refraction in monoaxial crystals earned him a fellowship that enabled him to spend 1926-1928 in Göttingen, working under Max Born. These were the decisive years in the formation of quantum mechanics, and the ideas and challenges that faced him in this period determined the course of Hylleraas’ entire scientific career. The next two years were spent partly in Oslo and partly in Göttingen, and in 1931 Hylleraas was made a member of the Christian Michelsen Institute in Bergen. In 1937 he followed Vilhelm Bjerknes as professor of theoretical physics at the University of Oslo, a chair he still occupied at his death. After World War II he was one of the Norwegian representatives at the Nordisk Institut for Teoretisk Atomfysikk (NORDITA) and in the Centre Européen de la Recherche Nucléaire (CERN). He spent 1947-1948 and 1962-1963 in the United States, at Princeton and the University of Wisconsin. Vigorous and hardworking until the day of his death, Hylleraas died of a heart attack in 1965. Aside from Sommerfild’s Atombau und Spektrallinien, which Hylleraas called “our student bible,” it was Born’s Dynamik der Kristallgitter that had the strongest influence on his early development. When he went to Göttingen in 1926, his intention was to continue his work in crystal lattice theory, which he in fact did for some time. Yet by 1926 Born had already moved into the new field of quantum mechanics, and it was only after some hesitation that Hylleraas followed his master. He had already earned a reputation as a very gifted mathematical physicist, and at Born’s suggestion he attacked the problem of the ionization energy of the ground state of the helium atom. The Bohr-Sommerfild theory had predicted the impossible value of about 28 electron volts, as against the experimental 24.46 electron volts; and it was thought that the helium problem would be the first real test of the Schrödinger equation. Hylleraas’ method of attack was significant for two reasons: first, the variational methods he introduced were largely his own and have since become standard techniques; second, to manage the very extensive calculations he used an electric Mercedes-Euklid calculating machine. This was probably the first time that machine calculation played an important part in physics; it has since become a standard mode of scientific activity. Hylleraas arrived at a value of 24.35 electron volts for the ionization energy; and this result was, as he put it:

...greatly admired and thought of as almost a proof of the validity of wave mechanics also in the strict numerical sense. The truth about it, however, was in fact that its deviation from the experimental value by an amount of one tenth of an electron volt was on the spectroscopic scale quite a substantial quantity and might as well have been taken to be a disproof ["Reminiscences"].

In 1929 he refined his own method through the introduction of new set of generalized coordinates and managed to achieve full agreement between theory and experiment.

Another spectacular early coup was the demonstration in 1930 of the theoretical stability of the negative hydrogen ion, although with characteristic modesty Hylleraas attributed this demonstration to Hans Bethe: “He—not I—is the father of that curious little child, the strange particle H—, which for a while appeared to be recognized nowhere, neither in heaven nor on earth.” A decade later the existence of H— in the solar atmosphere was definitely established.

Although Hylleraas always considered the helium atom and the negative hydrogen ion his special domains, over which he never really relinquished his hegemony, he contributed heavily and fundamentally to other areas of the quantum theory of atoms, molecules, and crystals. A very fine article on the wave mechanical treatment of lithium hydride (1930) is an amazing demonstration of the power of the Schrödinger equation and has remained a tour de force of twentieth-century physics. In the following years Hylleraas extended the application of wave mechanics to beryllium, boron, and carbon, most of this in connection with the experimental work of the Swedish spectroscopist Bengt Edlén. From the years 1935–1937 there is a set of fundamental articles on the energies, potential distributions, and spectra of diatomic molecules. Starting in the late 1930’s Hylleraas also contributed to nuclear physics, although most of his work in this field was never published. There are three long articles (1939–1943) on problems of tidal theory that fall outside his main area of interest. During the period 1945–1965 much of Hylleraas’ work was directed to secondary activities: reorganization of the University of Oslo and of the physics program, teaching, and editing. He still managed to turn out a number of significant articles, notably on scattering, on relativistic electron theory, and on spinors. During this time either he or one of his students kept the theory of the helium atom and the hydrogen ion up-to-date with the continuing experimental refinements.

As a physicist Hylleraas never possessed a transcending genius like, for instance, that of Bohr. His ability was mathematical, and indeed, he very nearly became a mathematician. His ingenuity and tenacity in forcing the mathematical solution of problems was amazing and recalls Sommerfeld, who was one of his heroes. The elegance and usefulness of many of Hylleraas’ methods—and indeed the extent to which they are now part of physics—are insufficiently appreciated. In his belief in the efficacy of a numerical and computational approach to physics, often combined with the use of calculating machines, he directly anticipated what is perhaps the main structure of modern science.

A modest, kind, and soft-spoken man, Hylleraas revealed a simplicity and humanity no doubt derived from a happy childhood, of which he spoke glowingly; and he always retained close ties with his native community. He trained two generations of theoretical physicists in Norway, and perhaps in retrospect his best efforts were directed toward teaching. He never shirked that part of his responsibility, and he worked long and fruitfully as a popularizer. In Norwegian physics he ranks second only to Bjerknes.

Hylleraas received a number of honorary degrees, memberships, and prizes. In 1963 the University of Florida arranged a symposium on atomic and molecular physics in his honor, and it was this event that probably brought him the greatest pleasure.

BIBLIOGRAPHY

I. Original Works. Hylleraas’ “Reminiscences From Early Quantum Mechanics of Two-Electron Atoms” is in “Proceedings of the International Symposium on Atomic and Molecular Quantum Mechanics in Honor of Egil A. Hylleraas,” in Review of Modern Physics, 35 , no. 3 (1963), 421; his Matematisk og Teoretisk Fysikk, 4 vols. (Oslo, 1950–1952) is now available in an American ed., Mathematical and Theoretical Physics (New York, 1970).

II. Secondary Literature. A short biography of Hylleraas, including a comprehensive bibliography, by O. K. Gjøtterud is in Nuclear Physics, 89 (1966), 1–10. The best biography and evaluation is H. Wergeland, “Egil A. Hylleraas 15.5. 1898–28.10.1965,” in Fra Fysikkens Verden, 28 (1966), 1–10.

Per StrØmholm