Meixner began his studies in theoretical physics with Arnold Sommerfeld at the Ludwig Maximilians University of Munich in 1926. He was awarded his doctorate in 1931, with the submission of a thesis on the application of the Green function in quantum mechanics.

After Sommerfeld’s death in 1951, Meixner edited a volume and new editions of two other volumes of Sommerfeld’s six-volume Vorlesungen über theoretische Physik.

Meixner conducted research and taught graduate courses at the Institut für theoretische Physik of the Rheinisch-Westfälische Technische Hochschule Aachen (RWTH Aachen). Literature citations, as well as doctorates granted to his students, put Meixner at RWTH Aachen, or just Aachen, for years in each of the decades from the 1950s until his death in 1994. He was known for his work on the physics of deformable bodies (rheology), thermodynamics, statistical mechanics, Meixner polynomials, Meixner-Pollaczek polynomials, and spheroidal wave functions.

• . This is Meixner’s doctoral thesis at Munich, submitted for publication 14 July 1931.

• . Meixner is cited as being at the Institut für theoretische Physik, RWTH Aachen. Received: 27 October 1972.

• . Meixner is cited as being at the Institut für Theoretische Physik, Rhein.-Westf. Technische Hochschule Aachen, Germany. Received: 19 May 1982.

• J. Meixner and F. W. Schafke Mathieusche Funktionen uns Sphäroidfunktionen (Springer-Verlag, 1954)
• J. Meixner, F. W. Schäfke, and G. Wolf Mathieu functions and spheroidal functions and their mathematical foundations: further studies (Springer-Verlag, 1980)

• J. Meixner, editor Statistical Mechanics of Equilibrium and Non-equilibrium Proceedings of the International Symposium on Statistical Mechanics and Thermodynamics held June 15-20, 1964, in Aachen, Germany. (North-Holland Publishing Co., 1965)

Sommerfeld, Arnold Vorlesungen über theoretische Physik. Band 5: Thermodynamik und Statistik. Herausgegeben von Fritz Bopp und Josef Meixner. (Diederich, 1952)

Sommerfeld, Arnold Vorlesungen über theoretische Physik. Band 2: Optik. 2. Auflage, bearbeitet und ergänzt von Fritz Bopp und Josef Meixner. (Akademische Verlagsgesellschaft, 1959)

Sommerfeld, Arnold Vorlesungen über theoretische Physik. Band 3: Elektrodynamik. 3. Auflage, bearbeitet und ergänzt von Fritz Bopp und Josef Meixner. (Akademische Verlagsgesellschaft, 1961)