Walter Kohn, whose parents saved his life by sending him out of Nazi-dominated Europe before the outbreak of World War II and who went on to become an American citizen and a winner of the Nobel Prize in chemistry for work vital in developing new materials for electronics and medicine, died April 19 at his home in Santa Barbara, Calif. He was 93.

His wife, Mara Kohn, daughter of the celebrated photographer Roman Vishniac, said he died of cancer.

Dr. Kohn, who was born into a Jewish family, was expelled from school in his native Austria after the Nazis annexed the country in 1938. His parents managed to send him and an older sister to safety in England on one of the last convoys of the Kindertransport rescue operation for refugee children. His father and mother later perished at the Auschwitz concentration camp.

Far from home and family, Dr. Kohn found himself with little to support him over a long period but his intellect and the goodwill of many strangers and mentors. Like other enemy aliens, he spent time in internment camps in England and Canada until beginning his higher education, capped by a doctorate in nuclear physics at Harvard.

At various times in his youth and early adulthood, he also worked on a farm, cut timber and prospected for gold. He also served a year in the Canadian army at the end of World War II.

With a good-natured demeanor that belied his many harsh experiences, he worked among the world’s top scientists at leading research institutions including the Niels Bohr Institute in Copenhagen and Bell Laboratories, where he was an assistant to William Shockley, a co-inventor of the transistor.

Dr. Kohn, whose honors also included the 1988 National Medal of Science, was regarded as an expert in mathematical physics, the physics of solids, and what is known as condensed matter physics.

Although he was known principally as a physicist, his 1998 Nobel was awarded in chemistry for work that embraced ideas and techniques from both disciplines. Scientists call the field quantum chemistry. It involved the applications of the discoveries and approaches of quantum mechanics to the interactions between chemical elements.

In the early 20th century, the novel and revolutionary ideas of quantum mechanics made it possible for the first time to explain the behavior of the hydrogen atom, the simplest in existence. It has a single electron orbiting its nucleus.

But the complexity of larger atoms and molecules, envisioned as possessing clouds of whirling electrons, remained for years a daunting challenge. Dr. Kohn was one of the foremost among those who applied advanced mathematical and quantum techniques to the problem of understanding the essence of complex chemical reactions.

Much of the scientific progress of the past 50 years entails the ma­nipu­la­tion of elements and compounds on the atomic and molecular scale. The work — much of it credited to the theoretical advances made by Dr. Kohn — helped scientists develop and create new molecules and new materials tailor-made for many purposes, including electronics and medicine.

In quantum chemistry, the area in which much of his work was done, an electron is both wave and particle, with the properties of each. Explaining the behavior of just one requires great mathematical sophistication. Describing the behavior of swarms of electrons by the same techniques as used for one was virtually beyond the reach of science.

Dr. Kohn was credited with finding a new technique for finding a way around the seeming intractability of the problem.

Sidestepping many mathematical pitfalls, his theory emphasized the total density of the charge of the electrons involved. It opened the way to deep insights into atomic and molecular behavior, and into the formation of chemical bonds.

In addition he worked on the physics of semiconductors, superconductivity, surface physics and catalysis.

Walter Kohn was born in Vienna on March 9, 1923, into a cultured middle-class family. His father operated a business that made and distributed high-quality postcards, for which he commissioned noted contemporary artists.

The Nazis’ annexation of Austria upended Dr. Kohn’s life. He arrived in England in 1939, staying with a family with whom his father had a business connection. But he was soon placed in an internment camp on the Isle of Man with many other adult “enemy aliens” who were deemed possible security threats amid the war rapidly consuming Europe.

He was transported by boat to Canada in 1940 to stay at a series of internment camps. “You couldn’t leave, but you were never maltreated in those camps,” he later told the Ottawa Citizen. “Working was, according to the Geneva Convention, optional. If you worked, you got 20 cents a day. Which was actually a lot of money.”

He spent the money he earned as a lumberjack on books about science, an interest fostered by many other Jewish camp internees who had fled the Nazis. He recalled one scholar, Fritz Rothberger, as a key mentor who “taught me mathematics and made it wonderful.”

Finally cleared of suspicion of being a Nazi spy, Dr. Kohn began studies at the University of Toronto, from which he received bachelor’s and master’s degrees in 1945 and 1946, respectively. At one point, he also held a summer job as a geophysicist, searching for — and, he noted, finding — gold in northern Ontario and Quebec.

A fellowship took him to Harvard, where he worked under Julian Schwinger, a future Nobel laureate in physics. Dr. Kohn received his PhD in 1948. Nine years later, he became an American citizen. He held faculty posts at Harvard, the Carnegie Institute of Technology in Pittsburgh (now Carnegie Mellon University) and the University of California at San Diego, where he chaired the physics department from 1961 to 1963.

He joined the faculty of the University of California at Santa Barbara in 1979 and remained there in various capacities until his death.

His first marriage, to Lois Adams, ended in divorce. In 1978, he married Mara Vishniac. Besides his wife, survivors include three daughters from his first marriage, Marilyn Kohn of San Francisco, Ingrid Paymar of Baltimore and Rosalind Dimenstein of Los Angeles; and three grandchildren.

The Nobel Prize — which he shared with mathematician and chemist John Pople of Northwestern University — brought him wide recognition. He told the Los Angeles Times that his contributions to science were his way of “trying to help live his lost family’s lives.”