- Person
- Hans Bethe
- Lived
- 1906–2005
- Field
- Theoretical physics
- From
- German-born American
The story
Most problems in quantum physics that involve many interacting particles cannot be solved exactly, so physicists have to rely on approximations. In 1931 the young German physicist Hans Bethe found a remarkable exception. He was then travelling on a Rockefeller fellowship, recommended by his teacher Arnold Sommerfeld, which took him first to Cambridge and then, in February 1931, to Enrico Fermi's laboratory in Rome. He was so impressed by Fermi that he regretted not having gone to Rome first.
Bethe, then 24, studied a one-dimensional model of magnetism: a chain of atoms whose spins interact with their neighbours, known today as the Heisenberg chain. A year earlier Felix Bloch had proposed a simplified form for its solutions, but it miscounted how many there should be. Bethe proposed the correct form and showed carefully that it produced exactly the right number of solutions. His paper, published in the Zeitschrift für Physik in 1931, gave the exact energies and quantum states of the chain. The approach became known as the Bethe ansatz, from the German word for an initial assumption about the form of an answer. Fermi's simplicity, together with Sommerfeld's rigour, shaped Bethe's own way of attacking problems.
For decades the method looked like a specialised trick, but from the late 1950s others began to build on it. In 1963 Elliott Lieb and Werner Liniger used it to solve a one-dimensional gas of interacting bosons. In 1966 C. N. Yang and C. P. Yang proved rigorously that it gives the ground state of the Heisenberg chain, and in 1968 Lieb and F. Y. Wu solved the one-dimensional Hubbard model, a basic model of electrons in solids. Around 1980 it was used to solve models of magnetic impurities in metals.
The method was later generalised into the quantum inverse scattering method, also called the algebraic Bethe ansatz, which forms the basis of the modern theory of integrable systems. Several models solvable by the Bethe ansatz have now been realised in experiments, both in solid materials and in optical lattices, where ultracold atoms are trapped by laser light. When Richard Feynman died in 1988, "Bethe ansatz problems" were listed on his blackboard among the things he still wanted to learn.
Why it matters
Bethe's method gives scientists rare exact solutions that serve as benchmarks for understanding magnetism, quantum materials and ultracold atoms.
About Hans Bethe
Refugee physicist who explained how the stars shine, led theory at Los Alamos, cracked the Lamb shift and spent half a century campaigning against the nuclear arms race; Nobel Prize 1967.
More about Hans Bethe
- Hans Bethe championed peaceful nuclear energyThroughout the 1980s and 1990s Hans Bethe campaigned for the peaceful use of nuclear energy, calling nuclear electricity 'a necessity, not merely an option'.
- 'Bethe's Bible' taught a generation nuclear physicsIn 1936–37 Hans Bethe, with Robert Bacher and Stanley Livingston, wrote three review articles so complete they became known as 'Bethe's Bible'.
- Hans Bethe explained how the stars shineIn 1938–39 Hans Bethe worked out the nuclear reactions that power the Sun and stars, work that won him the 1967 Nobel Prize in Physics.
- The Bethe formula tracks radiation through matterIn 1930 Hans Bethe derived a formula for how fast charged particles lose energy passing through matter, still used across physics today.
- Bethe showed missile defence could be fooled by decoysIn 1968 Hans Bethe and Richard Garwin argued that missile defences could be defeated by simple decoys, an argument that helped lead to the 1972 ABM Treaty.
- Hans Bethe helped secure the 1963 Test Ban TreatyHans Bethe served on the President's Science Advisory Committee from 1956 to 1964 and helped bring about the 1963 treaty banning atmospheric nuclear tests.
- Hans Bethe cracked the Lamb shift on a trainIn 1947, on a train to Schenectady, Hans Bethe calculated the Lamb shift, showing quantum electrodynamics could work and opening modern particle physics.
- At 85, Hans Bethe helped solve the solar neutrino puzzleAt the age of 85, Hans Bethe wrote an important paper on the solar neutrino problem, helping establish that neutrinos change type on their way from the Sun.
Sources
- Hans Bethe Wikipedia
- Bethe ansatz Wikipedia
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