Hans Albrecht Eduard Bethe (; German: [ˈhans ˈbeːtə] ; 2 July 1906 – 6 March 2005) was a German-American physicist who made major contributions to nuclear physics, astrophysics, quantum electrodynamics and solid-state physics, and received the Nobel Prize in Physics in 1967 for his work on the theory of stellar nucleosynthesis. For most of his career, Bethe was a professor at Cornell University.
In 1931, Bethe developed the Bethe ansatz, which is a method for finding the exact solutions for the eigenvalues and eigenvectors of certain one-dimensional quantum many-body models. In 1939, Bethe published a paper which established the CNO cycle as the primary energy source for heavier stars in the main sequence classification of stars, which earned him a Nobel Prize in 1967. During World War II, Bethe was head of the Theoretical Division at the secret Los Alamos National Laboratory that developed the first atomic bombs. There he played a key role in calculating the critical mass of the weapons and developing the theory behind the implosion method used in both the Trinity test and the "Fat Man" weapon dropped on Nagasaki in August 1945.
After the war, Bethe played an important role in the development of the hydrogen bomb, as he also served as the head of the theoretical division for the project, although he had originally joined the project with the hope of proving it could not be made. He later campaigned with Albert Einstein and the Emergency Committee of Atomic Scientists against nuclear testing and the nuclear arms race. He helped persuade the Kennedy and Nixon administrations to sign, respectively, the 1963 Partial Nuclear Test Ban Treaty and 1972 Anti-Ballistic Missile Treaty (SALT I). In 1947, he wrote an important paper which provided the calculation of the Lamb shift, which is credited with revolutionizing quantum electrodynamics and further "opened the way to the modern era of particle physics". He contributed to the understanding of neutrinos and was key in the solving of the solar neutrino problem. He contributed to the understanding of supernovas and their processes.
His scientific research never ceased, and he was publishing papers well into his nineties, making him one of the few scientists to have published at least one major paper in his field during every decade of his career, which in Bethe's case spanned nearly seventy years. Physicist Freeman Dyson, once his doctoral student, called him "the supreme problem-solver of the 20th century", and cosmologist Edward Kolb called him "the last of the old masters" of physics.
Bethe was born in Strasbourg, which at the time was part of the Reichsland Elsaß-Lothringen, Germany, on July 2, 1906, the only child of Anna (née Kuhn) and Albrecht Bethe, a Privatdozent of physiology at the University of Strasbourg. Although his mother, the daughter of Abraham Kuhn, professor at the University of Strasbourg, had a Jewish background, Bethe was raised Protestant, like his father; and he became an atheist later in life.
His father accepted a position as professor and director of the Institute of Physiology at Kiel University in 1912, and the family moved into the director's apartment at the institute. Initially, he was schooled privately by a professional teacher as part of a group of eight girls and boys. The family moved again in 1915 when his father became the head of the new Institute of Physiology at the University of Frankfurt am Main.
Bethe attended the Goethe-Gymnasium in Frankfurt, Germany. His education was interrupted in 1916, when he contracted tuberculosis, and he was sent to Bad Kreuznach to recuperate. By 1917, he had recovered sufficiently to attend the local Realschule and the following year, he was sent to the Odenwaldschule, a private, coeducational boarding school. He attended the Goethe-Gymnasium again for his final three years of secondary schooling, from 1922 to 1924.
Having passed his Abitur, Bethe entered the University of Frankfurt in 1924. He decided to major in chemistry. The instruction in physics was poor, and while there were distinguished mathematicians in Frankfurt such as Carl Ludwig Siegel and Otto Szász, Bethe disliked their approaches, which presented mathematics without reference to the other sciences. Bethe found that he was a poor experimentalist who destroyed his lab coat by spilling sulfuric acid on it, but he found the advanced physics taught by the associate professor, Walter Gerlach, more interesting. Gerlach left in 1925 and was replaced by Karl Meissner, who advised Bethe that he should go to a university with a better school of theoretical physics, specifically the Ludwig-Maximilians-Universität München, where he could study under Arnold Sommerfeld.
Bethe entered the Ludwig-Maximilians-Universität München in April 1926, where Sommerfeld took him on as a student on Meissner's recommendation. Sommerfeld taught an advanced course on differential equations in physics, which Bethe enjoyed. Because he was such a renowned scholar, Sommerfeld frequently received advance copies of scientific papers, which he put up for discussion at weekly evening seminars. When Bethe arrived, Sommerfeld had just received Erwin Schrödinger's papers on wave mechanics.
For his PhD thesis, Sommerfeld suggested that Bethe examine electron diffraction in crystals. As a starting point, Sommerfeld suggested Paul Ewald's 1914 paper on X-ray diffraction in crystals. Bethe later recalled that he became too ambitious, and, in pursuit of greater accuracy, his calculations became unnecessarily complicated. When he met Wolfgang Pauli for the first time, Pauli told him: "After Sommerfeld's tales about you, I had expected much better from you than your thesis." "I guess from Pauli," Bethe later recalled, "that was a compliment."
After Bethe received his doctorate, Erwin Madelung offered him an assistantship in Frankfurt, and in September 1928 Bethe moved in with his father, who had recently divorced his mother. His father had met Vera Congehl earlier that year and married her in 1929. They had two children, Doris, born in 1933, and Klaus, born in 1934.
Bethe did not find the work in Frankfurt very stimulating, and in 1929 he accepted an offer from Ewald at the Technische Hochschule Stuttgart. While there, he wrote what he considered to be his greatest paper, Zur Theorie des Durchgangs schneller Korpuskularstrahlen durch Materie ("The Theory of the Passage of Fast Corpuscular Rays Through Matter"). Starting from Max Born's interpretation of the Schrödinger equation, Bethe produced a simplified formula for collision problems using a Fourier transform, which is known today as the Bethe formula. He submitted this paper for his habilitation in 1930.
Sommerfeld recommended Bethe for a Rockefeller Foundation Travelling Scholarship in 1929. This provided $150 a month (about $3,000 in 2025 dollars) to study abroad. In 1930, Bethe chose to do postdoctoral work at the Cavendish Laboratory at the University of Cambridge in England, where he worked under the supervision of Ralph Fowler. At the request of Patrick Blackett, who was working with cloud chambers, Bethe created a relativistic version of the Bethe formula.
Bethe was known for his sense of humor, and with Guido Beck and Wolfgang Riezler, two other postdoctoral research fellows, created a hoax paper On the Quantum Theory of the Temperature of Absolute Zero where he calculated the fine structure constant from the absolute zero temperature in Celsius units. The paper poked fun at a certain class of papers in theoretical physics of the day, which were purely speculative and based on spurious numerical arguments, such as Arthur Eddington's attempts to explain the value of the fine structure constant from fundamental quantities in an earlier paper. They were forced to issue an apology.
For the second half of his scholarship, Bethe chose to go to Enrico Fermi's laboratory in Rome in February 1931. He was greatly impressed by Fermi and regretted that he had not gone to Rome first. Bethe developed the Bethe ansatz, a method for finding the exact solutions for the eigenvalues and eigenvectors of certain one-dimensional quantum many-body models. He was influenced by Fermi's simplicity and Sommerfeld's rigor in approaching problems and these qualities influenced his own later research.