Heisenberg group Heisenberg group In mathematics, the Heisenberg group formula_1, named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form under the operation of matrix multiplication. Elements "a, b" and "c" can be taken from any commutative ring with identity, often taken to be the ring of real numbers (resulting in the "continuous Heisenberg group") or the ring of integers (resulting in the "discrete Heisenberg group"). The continuous Heisenberg group arises in the description of one-dimensional quantum mechanical systems, especially in the context of the Stone–von Neumann theorem. More generally, one can consider Heisenberg groups associated to
Werner Heisenberg here is a memoir in the form of rationally reconstructed dialogue. And the dialogue as Galileo well knew, is itself a most insidious literary device: lively, entertaining, and especially suited for insinuating opinions while yet evading responsibility for them." Few scientific memoirs had been published, but Konrad Lorenz and Adolf Portmann had penned popular books that conveyed scholarship to a wide audience. Heisenberg worked on his autobiography with the publisher Piper in Munich and initially proposed the title "Gespräche im Umkreis der Atomphysik" ("Conversations around atomic physics"). He settled with his publisher on "Der Teil und das Ganze" ("The part