Migdal was a postdoc at the Leningrad Institute of Physics and Technology, where his supervisor was Matvei Bronstein,[3] and Yakov Frenkel was the chief of the theory department.
[2] From 1938 Migdal worked with Lev Landau at Moscow's Institute for Physical Problems, received there in 1943 his Russian Doctor of Sciences degree (habilitation), and was employed there until 1945.
In 1944 Migdal also became a professor at National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) (Национальный исследовательский ядерный университет "МИФИ", MIFI).
From 1971 until his death in 1991 Migdal was a professor at the Landau Institute for Theoretical Physics of the Academy of Sciences of the Soviet Union in Moscow.
At a meeting on November 30, 1945, instructions were given to a group of scientists, including Migdal, Abram Alikhanov (as chair), Lev Landau, Yulii Khariton, Samuil Reinberg, Mikhail Sadovsky, Sergei Sergeyevich Vasilyev, and Aleksandr Zakoshchikov, to analyze all available materials on the consequences of the use of atomic bombs in Hiroshima and Nagasaki and to determine the effectiveness of the blast factor, heat factor, and radiation factor.
At that time, every physicist supposed that it was the main and the most important part of theoretical physics, metal theory.In 1942 Artem Alikhanian and Abram Alikhanov went on an expedition into Yerevan to study cosmic rays.
Toward the end of WWII, Landau, Pomeranchuk, and Migdal did some theoretical research on cosmic rays, concerning the theory of Auger showers.