Heisenberg group by 90°. The other reflections are "xyx" and "yxy", and rotation by 180° is "xyxy" (="yxyx"). The Lie algebra formula_16 of the Heisenberg group formula_1 (over the real numbers) is the space of formula_18 matrices of the form with formula_20. The following three elements form a basis for formula_16: The basis elements satisfy the commutation relations: The name "Heisenberg group" is motivated by the preceding relations, which have the same form as the canonical commutation relations in quantum mechanics: where formula_25 is the position operator, formula_26 is the momentum operator, and formula_27 is Planck's constant. The Heisenberg group formula_1 has
Institute of Physics when the expansion of access to universities removed demand. In 1960, the Physical Society and the Institute of Physics merged, creating a single organization with the unwieldy name "The Institute of Physics and the Physical Society", which combined the learned society tradition of the Physical Society with the professional body tradition of the Institute of Physics. Under the leadership of Thomas E. Nevin an Irish branch of the Institute of Physics was formed in 1964. Upon being granted a royal charter in 1970, the organization was renamed as the Institute of Physics. There are four grades of membership: Associate Member,