THE UNCERTAINTY PRINCIPLE ON CAYLEY-GRAPHS

Heisenberg's uncertainty principle is extended to certain finite graph s. The fundamental theorem of calculus, integration by parts, and vani shing boundary terms for graphs are defined as well as functions of ra ndom variables, expectation values, and moments on graphs. Section 3 g ives three versions of Heisenberg's uncertainty principle for graphs. For the 2nd version, we assume that our graph is the Cayley graph of a finite abelian group. We work out the example of a finite cycle graph in detail and compare it to the uncertainty principle on the continuo us circle obtained by Grunbaum around 1990.