Müller then enrolled in the Physics and Mathematics Department of the Swiss Federal Institute of Technology (ETH Zürich).

After receiving his Diplom, he worked for one year, then returned to ETH Zürich for a PhD, submitting his thesis at the end of 1957.

Müller joined the Battelle Memorial Institute in Geneva, soon becoming the manager of a magnetic resonance group.

In 1987 (before winning the Nobel Prize) he got an honorary degree (laurea honoris causa) in Physics from the University of Pavia.

Between his undergraduate degree and beginning his graduate studies, he worked for one year in the Department of Industrial Research at ETH on the Eidophor large-scale display system.

The highest critical temperature (Tc) attainable at that time was about 23 K. In 1983 Müller recruited Georg Bednorz to IBM, to help systematically test various oxides.

A few recent studies had indicated these materials might superconduct, but experts who knew about Müller's idea thought it was “crazy”.

A couple of months later Chu achieved superconductivity at 93 K in YBCO, triggering a stampede of scientific interest exemplified by the 1987 "Woodstock of physics", at which Müller was a featured presenter.