Abstract

Heisenberg’s uncertainty principle is extended to certain finite graphs. The fundamental theorem of calculus, integration by parts, and vanishing boundary terms for graphs are defined as well as functions of random variables, expectation values, and moments on graphs. Section 3 gives 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 continuous circle obtained by Grünbaum around 1990.

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