Merzbacher was born in Berlin. Being a Jew, he emigrated in 1935 with his family from Germany to Turkey, where his father worked as a chemist. He received his licentiate from University of Istanbul in Turkey in 1943 and taught high school in Ankara for the next four years. In 1947 he moved to the United States to attend Harvard University, where he earned his M.A. (1948) and his Ph.D. with Julian Schwinger in 1950. During 1950/51, he worked at the Institute for Advanced Study. In 1951-52, Merzbacher was a visiting assistant professor at Duke University. In 1952 he joined the faculty of the University of North Carolina in Chapel Hill. In 1959/60, he worked at the Institute of Theoretical Physics in Copenhagen, where he became closely acquainted with Niels Bohr; in 1967/68 he was visiting professor at the University of Washington in Seattle. In 1977 he was the recipient of a U. S. Senior Scientist Humboldt Award at the University of Frankfurt. In 1986 he was a Visiting Research Fellow at the Universities of Edinburgh and Stirling in Scotland. In 1991 he was Arnold Bernhard Visiting Professor at Williams College. In 1992 he received the Oersted Medal from the American Association of Physics Teachers. In 2009 Merzbacher was the recipient of the Francis Slack Award from the Southeastern Section of the American Physical Society.
Merzbacher's research has been in applications of quantum mechanics to atomic and nuclear collision theory. He was a co-founder of the Triangle Universities Nuclear Laboratory, supported by the U.S. Department of Energy.
From 1977 to 1982 he served as chairman of the Department of Physics at the University of North Carolina Chapel Hill (UNC). He was named a Kenan Professor in 1969. He received UNC's 1972 Thomas Jefferson Award. Merzbacher is probably best known for his influential graduate level quantum mechanics textbook, which has so far seen three editions, the most recent in 1998. He married Ann Townsend Reid and together they had four children: Celia, Charles, Matthew and Mary (deceased). Merzbacher retired in 1991. In 1990, he was President of the American Physical Society. In 1993, UNC presented him with an honorary doctorate in science.
- Quantum Mechanics, John Wiley, 1961, 1970, 3rd edition (completely revised) 1998, ISBN 0-471-88702-1
- "Eugen Merzbacher | Death Notices". NewsObserver.com. 2013-06-09. Archived from the original on 2013-06-18. Retrieved 2013-06-21.
- "Eugen Merzbacher". Array of Contemporary American Physicists. American Institute of Physics. Archived from the original on December 11, 2015. Retrieved November 16, 2011.