Müller worked at the Siemens Research Laboratory, where he invented the field emission microscope in 1936 that allowed resolutions of 2 nanometers.
In 1947, he was appointed to the Kaiser Wilhelm Institute for Physical Chemistry and Electrochemistry (renamed to Fritz-Haber-Institut on the occasion of its incorporation into the Max Planck Society in 1953) by Iwan N. Stranski.
Here he developed the field ion microscope which, due to its resolution of 0.25 nm, was the first instrument used to observe atoms.
In 1950, he took a teaching appointment at Technische Universität Berlin after finally having completed the required Privatdozent (habilitation).
Müller joined the faculty at Pennsylvania State University in 1952, where he remained until his death in 1977.