Weidenmüller is known above all for his work in the theory of nuclear reactions. He examined nuclear reactions in the shell model under inclusion of continuum states and developed a microscopic statistical theory of nuclear reactions; this statistical theory (now known as transport theory) had applications to the interpretation of the particle accelerator experiments with heavy ions as well as on highly excited compound nuclei. He also examined chaotic dynamism in atomic nuclei and nuclear reactions (as well as Bose–Einstein condensates) with the help of the method of random matrices.