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 – 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 can’t be done, can be done, and whether it can or can’t be done in a sophisticated mathematical framework created by Murray and von Neumann. In the second talk, Zhe Liu will “close the noose.” (See her abstract for more.)

Title: The von Neumann – 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 “classic” representation, with emphasis on the differentiation operator on the real line. We discuss its meaning and domain and special “cores.” 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.