In 1964, under John Hopfield at the University of California, Berkeley he received his PhD in physics for explaining linear dispersion in excitations.
While at Oregon he continued his work on the x-ray edge and expanded it to include surface science and the microscopic theory of dielectrics.
During Lamar Alexander's tenure as President of the University of Tennessee, he recruited Mahan to teach freshman physics, which he did for ten years.
In his role as chairman of ICCMP he traveled relentlessly to foster collaboration between South American and US and European physicists.
While at GE, Mahan pioneered the application of mathematical techniques developed by three Russians: Alexei Abrikosov, Lev Gor'kov and Igor Dzyaloshinskii; to adapt Green's functions to theoretical solid-state physics.
Charles Duke worked closely with Mahan while they were both at GE and learned and applied these techniques leading to discoveries in the tunneling of electrons across semiconductor diodes.
He developed mathematical models that explained how varistors function (they are extremely non-linear devices) leading to substantial improvements in their effectiveness.
He worked closely with Lloyd Chase and did the first Raman scattering of beta-alumina which is used to make high-density solid-state batteries.
He later wrote a book on the subject with Kumble Subbaswammy (a former PhD student) titled Local Density Theory of Polarizability.
In Penn State University, he worked with Peter Eklund on vibrational properties of carbon nanotubes and silicon nanowires.