Lawrence C. Biedenharn

(November 18, 1922–February 12, 1996)

Lawrence Christian Biedenharn, Jr., a prominent mathematical physicist, was born on November 18, 1922, in Vicksburg, Mississippi. He attended the Massachusetts Institute of Technology in Cambridge, Massachusetts, served in the Armed Forces as First Lieutenant, US Army Signal Corps from 1942 until 1946, receiving his BS degree in absentia in 1944. He was stationed in the Pacific close to the Japanese surrender, and afterwards he was a radio officer for a year in Tokyo. From there he applied to graduate school at MIT, where he obtained his PhD degree in 1950. He was supervised by a famous theorist, Victor Weisskopf, while also working with John Blatt.

Prior to coming to Duke University as a full Professor in 1961, he was a research physicist at the Oak Ridge National Laboratory in Tennessee, Assistant Professor at Yale University and Associate Professor at Rice University. He became James B. Duke Professor in 1987 and Emeritus at the age of seventy in 1992. He then moved to the University of Texas in Austin, where he became Adjunct Professor and continued to teach. He died in Austin of kidney cancer on February 12, 1996.

Biedenharn has made major contributions to the understanding of the role of angular momentum in nuclear reactions and to the theory of excitations in nuclei via the electromagnetic force. Two articles co-authored by Biedenharn with John Blatt and M.E. Rose in the prestigious *Reviews of Modern Physics* are among the 100 most cited RMP papers in the period between 1955 and 1985. This came as information from its editor, David Pines, who in 1986 asked Biedenharn to submit another paper “to try for yet another classic”. His book in 1965 on *Coulomb Excitations*, co-authored with Pieter Brussaard – who was his postdoctoral associate prior to becoming Professor of Physics at the University of Utrecht in the Netherlands – is an often quoted work. This was the beginning of a very successful series of collaborations with prominent theorists from all over the world who visited Duke and wrote articles and books with him. Such “classic” books were *Angular Momentum in Quantum Physics* and *Racah-Wigner Algebra in Quantum Theory *(1981) both with J.D. Louck, which are still authoritative sources on the theory of angular momentum in quantum mechanics. His influential paper on the *Quantum Group Symmetry SU(2)-q* in 1989 was followed by the book on the same subject including q-Tensor Algebras, coauthored with Max Lohe, a visiting professor from the University of Adelaide in Australia and appeared only a few months before his death. Biedenharn’s greatest impact has been in the domain of mathematical physics, and he has published many papers emphasizing and developing the concept of symmetry and discreteness by means of which physics can be exploited mathematically. He was a grand master in group theory and quantum mechanics. A list of his articles and books is available here.

He also trained 24 PhD students, and several of them became prominent in turn. He attracted bright postdoctoral associates and had many visiting colleagues with whom he collaborated on articles and books. The productivity and impact of this theoretical group were substantial.

Larry Biedenharn’s many professional activities besides his teaching and research included membership and past chairmanship on a number of national advisory and prize committees, and on a National Academy of Science review committee. In particular, he was the chairman and member for many years of the Eugene Wigner Prize committee on group theory. From 1985 until 1993, he was the editor of the *Journal of Mathematical Physics.
*

He received many honors, among them both Fulbright and Guggenheim awards in 1958, the Alexander von Humboldt Foundation Senior Scientist Award (in 1976 and 1987), the Jesse Beams Medal of the American Physical Society and countless fellowships and lecturerships abroad.

Larry met his future wife Sarah Willingham in 1949, when she was a junior at Wellesley College and he was completing his PhD thesis at the MIT. They were married in spring 1950, the year Sarah graduated and began her studies of law at the University of Tennessee, transferring to Yale, when Biedenharn was appointed to the faculty there. She received her LLD from Yale in 1954. They raised two children, John and Sally. Sarah was an invaluable asset to her husband, often accompanying him on his many professional travels and by being a generous host to his graduate students and visitors. Larry told the story that while at MIT he made, at that time, a desperate – it turns out successful – effort to lose his strong southern drawl. Nobody in the institutions where he subsequently occupied a position could believe that he hailed from the Deep South.

Sarah and Larry Biedenharn, Salamanca, Spain, 1992. (photo from Y. S. Kim's website)

**Article from Duke University Physics Web Site**

Lawrence C. Biedenharn Jr., 73, a longtime member of Duke University's physics faculty and an internationally known researcher in theoretical physics, died Monday, Feb. 12, in Austin, Texas, after a lengthy battle with cancer. He had made his home in Texas in recent years.

Biedenharn became the youngest full professor on the Duke faculty—at age 38—when he was appointed in 1961. He remained at Duke until 1993, when he retired as James B. Duke professor of physics and subsequently moved to the University of Texas at Austin as adjunct professor. A native of Vicksburg, Miss., he received both his bachelor's degree and his Ph.D. from the Massachusetts Institute of Technology and served in World War II as a Signal Corps officer and later on the staff of Gen. Douglas MacArthur in Japan.

Serving on the faculties of Yale University and Rice University before coming to Duke, he published six books and hundreds of research articles in the fields of nuclear physics and later mathematical physics. He also edited the *Journal of Mathematical Physics* for many years.

Biedenharn, Holman, and Louck showed how the classical work on ordinary hypergeometric series is intimately related to the irreducible representations of the compact group SU(2). Similarly, they found U(n) multiple series generalizations of one-variable hypergeometric summation and transformation theorems by comparing two ways of computing the matrix elements of multiplicity free Wigner and Racah coefficients in U(n). This work was done in the context of the quantum theory of angular momentum and the special unitary groups SU(n). This work motivated the far-reaching q-analogs that Milne, Gustafson, and their co-workers subsequently found. Applications of this later work include unified proofs of the Macdonald identities, constant term identities, multiple q-beta integrals, U(n+1) and symplectic generalizations of the Bailey Transform and Bailey Lemma, classical matrix inversion results, numerous classical summation and transformation theorems for one-variable q-series, Rogers-Ramanujan identities, and, finally, new infinite families of identities for sums of squares in classical number theory.

His book, *Quantum Group Symmetry and q-tensor Algebras*, jointly written with M.A. Lohe, appeared recently; see *OP-SF NET, Issue 3.2, Topic #9*. Biedenharn's work continues to motivate much of this recent research in multivariable orthogonal polynomials, special functions, and their applications.

Lawrence C. Biedenharn is survived by his wife of 45 years, Sarah; his son John; daughter Sally; and two grandchildren.

**Obituary for Sarah W. Biedenharn**

AUSTIN, Texas —** Sarah Willingham Biedenharn **was born Nov. 3, 1929, in Richmond, Va., to Harris and Lynn Lewis Willingham. She died Nov. 2, 2011, in Austin, Texas, where she had been a resident for many years.

She married Lawrence C. Biedenharn Jr. in 1950, just before graduating from Wellesley College. While he was on the Yale physics faculty, she received her JD from the Yale Law School. They lived in Houston while Larry was an associate professor of physics at Rice University, and she became a member of the Texas Bar Association. They moved in 1961 to Durham, N.C., where he was a professor of physics at Duke University. Sarah got her private pilot’s license in 1989. They had extended stays in Copenhagen, Geneva, Frankfurt, Palo Alto, Austin and Los Alamos when Larry visited other research facilities. They finally moved to Austin in 1992 when he retired and became an adjunct professor at the University of Texas at Austin.

Sarah was widowed in 1996 after 46 years of a very happy marriage. She loved living in Austin and especially at Querencia. She was an active member of the Episcopal Church of the Good Shepherd. She was a board member of Caritas for many years and an enthusiastic supporter of the Foundation for Women’s Cancer, Safe Place, Wellesley College and the building of the Long Center. She was one of Austin’s Perfect Ten in 2007. She enjoyed a great many trips throughout the world. Friends and family gave her much pleasure.

She is survived by her children, John Biedenharn and his wife, Tina, of Sunset Beach, Calif., and Sally Biedenharn of Destin, Fla.; her grandchildren, Lauren and Johnny; her brother, Harris Willingham Jr.; her brother-in-law, Robert Biedenharn; and many nieces and nephews.

**The Lawrence Biedenharn Papers**

By Carol Mead

The following article, featured as part of the *Archives of American Mathematics Spotlight*, was published in the November 2008 issue of *MAA FOCUS*. The full issue is available here (pdf).

The *Archives of American Mathematics (AAM)* has recently processed and made available the papers of prominent mathematical physicist Lawrence Christian Biedenharn, recognized worldwide as one of the leaders of modern theoretical physics. They consist of Biedenharn's notes, publications, conference talks, teaching materials from Duke University, correspondence, and personal documents. Biedenharn's wife, Sarah, donated the papers to the University of Texas at Austin in 2007. A finding aid is available online.

Biedenharn was born in Vicksburg, Mississippi, in 1922. His undergraduate studies at the Massachusetts Institute of Technology (MIT) were interrupted by World War II, which he spent in the U.S. Army Signal Corps. He received his bachelor of science degree in absentia from MIT in 1944 and applied for graduate studies at MIT while stationed in Tokyo in 1946. He returned to MIT in 1946 and completed his PhD in theoretical nuclear physics in 1950.

After graduation, Biedenharn worked for two years as a research assistant at the Oak Ridge National Laboratory in Tennessee. His teaching career began in 1952 when Yale University hired him as an assistant professor. He joined the faculty at Rice University in 1954, becoming an assistant professor there in 1956. Five years later, he moved to Duke University, where he became the youngest full professor on the Duke faculty at age 38. He worked at Duke, supervising 24 PhD students, until becoming Emeritus in 1992. At that time, Biedenharn moved to the University of Texas at Austin, where he continued to teach as an adjunct professor until his death from cancer in 1996.

Throughout his life, Biedenharn received many honors and awards, including the Fulbright and Guggenheim awards in 1958, and the Alexander von Humboldt Foundation Senior Scientist Award in 1976 and 1987. Biedenharn's 70th birthday was celebrated with a symposium held in his honor in Bregenz, Austria. The journal *Foundations of Physics* published a memorial edition dedicated to Biedenharn in 1997. The University of Texas at Austin established the Lawrence C. Biedenharn Endowed Chair in Physics with a gift by Sarah Biedenharn to honor her husband's contributions to theoretical physics.

Biedenharn's colleagues and his many students knew him as an intelligent, cultured man with varied interests. In addition to his extensive scientific work, which continued unabated throughout the years, and even increased toward the end of his life, Biedenharn pursued many other interests. Among other things, he had a great love for music, particularly chamber music.

The highlight of the Biedenharn papers is his serial notes. Over the course of almost 50 years, Biedenharn kept research notes related to his work on symmetries in nuclear physics, time reversal, relativistic quantum mechanics, and Coulomb excitation, about all of which he wrote and published extensively. Also included in the serial notes are printed materials related to his teaching activities and his participation in various conferences around the world.

Page from Biedenharn's serial notes "I," 1962.

Source: The Lawrence Biedenharn Papers at the Archives of American Mathematics.

In addition to the serial notes, the collection contains copies of hundreds of his research articles in the fields of nuclear physics and later mathematical physics along with related notes, his conference talks covering a span of 40 years, and his teaching materials used at Duke University. The personal series of the papers includes his thesis from MIT, military service documents, personal correspondence, the proceedings of a symposium in honor of Biedenharn, and the memorial issue of the *Foundations of Physics* journal dedicated to Biedenharn.

Larry Biedenharn and Eugene Wigner, 1988, (Photo from Y. S. Kim's website)