Werner Heisenberg foundation of the matrix formulation of quantum mechanics through only the use of observables. In February 1943, Heisenberg was appointed to the Chair for Theoretical Physics at the "Friedrich-Wilhelms-Universität" (today, the Humboldt-Universität zu Berlin). In April, his election to the "Preußische Akademie der Wissenschaften" (Prussian Academy of Sciences) was approved. That same month, he moved his family to their retreat in as Allied bombing increased in Berlin. In the summer, he dispatched the first of his staff at the "Kaiser-Wilhelm Institut für Physik" to Hechingen and its neighboring town of Haigerloch, on the edge of the Black Forest, for the
Heisenberg group a group, as is shown by the multiplication: and The Heisenberg group is a simply-connected Lie group whose Lie algebra consists of matrices where By letting e, ..., e be the canonical basis of R, and setting the associated Lie algebra can be characterized by the canonical commutation relations, where "p", ..., "p", "q", ..., "q", "z" are the algebra generators. In particular, "z" is a "central" element of the Heisenberg Lie algebra. Note that the Lie algebra of the Heisenberg group is nilpotent. The exponential map is given by the following expression The exponential map of a nilpotent Lie