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 Hahn and Carl Friedrich von Weizsäcker, were glad the Allies had won World War II. Heisenberg told scientists that he had never contemplated a bomb, only an atomic pile to produce energy. The morality of creating a bomb for the Nazis was also discussed. Only a few of the scientists expressed genuine horror at the prospect of nuclear weapons, and Heisenberg himself was cautious in discussing the matter. On the failure of the German nuclear weapons program to build an atomic bomb, Heisenberg remarked: "We wouldn't have had the moral courage to recommend to the Government in the spring of