Weidenmüller studied in Bonn and from 1956 to 1957 in Heidelberg under J. Hans D. Jensen, who was his doctoral thesis advisor for his thesis on stripping reactions (Zeitschrift für Physik Bd.150, 1958, 389), in which the nuclei used as projectiles lose nucleons to the nuclei used as targets. He was from 1963 professor for theoretical physics at the University of Heidelberg. From 1968 he worked at the Max Planck Institute for Nuclear Physics and was director there from 1972 until his 2001 retirement.