 
Summary: DISCRETIZED CCR ALGEBRAS
William Arveson
Department of Mathematics
University of California
Berkeley CA 94720, USA
To the memory of John Bunce
Abstract. We discuss how the canonical commutation relations must be modified
in order to make appropriate numerical models of quantum systems. The Calgebras
associated with the discretized CCRs are the noncommutative spheres of Bratteli,
Elliott, Evans and Kishimoto.
1991 Mathematics Subject Classification. Primary 46L40; Secondary 81E05.
Key words and phrases. Calgebras, commutation relations, quantum mechanics.
This research was supported in part by NSF grant DMS8912362
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2 WILLIAM ARVESON
1. Introduction.
We consider the problem of discretizing the Hamiltonian of a onedimensional
quantum system in a form that is appropriate for carrying out numerical studies.
Specifically, we start with a formal Schršodinger operator
