Title: The Heisenberg-von Neumann Puzzle
This talk will be the first of two (brief) talks. The first talk (by R. Kadison), will discuss the Heisenberg relation, QP â PQ = (-ih/2pi) I, from the point of view of quantum mechanics, and the attempt to place it in a mathematical framework. We shall study when this canât be done, can be done, and whether it can or canât be done in a sophisticated mathematical framework created by Murray and von Neumann. In the second talk, Zhe Liu will âclose the noose.â (See her abstract for more.)
Title: The von Neumann â Heisenberg Puzzle
In the second talk on this topic, we study the representation of the basic Heisenberg relation by unbounded operators on a Hilbert space with special attention to the domains of those operators. We consider, first, the âclassicâ representation, with emphasis on the differentiation operator on the real line. We discuss its meaning and domain and special âcores.â We introduce approximation by special polynomials for these purposes. We then move to the question of representing the relation in the way von Neumann had wanted.