Summary: NON-COMMUTATIVE SPHERES AND
NUMERICAL QUANTUM MECHANICS
Department of Mathematics
University of California
Berkeley CA 94720, USA
Abstract. We discuss some basic issues that arise when one attempts to model
quantum mechanical systems on a computer, and we describe the mathematical
structure of the resulting discretized cannonical commutation relations. The C-
algebras associated with the discretized CCRs are the non-commutative spheres of
Bratteli, Elliott, Evans and Kishimoto.
1991 Mathematics Subject Classification. Primary 46L40; Secondary 81E05.
Key words and phrases. C-algebras, commutation relations, quantum mechanics.
Contributed to the proceedings of a NATO conference on operator algebras, mathematical
physics and low dimensional topology, held in Istanbul, 15 July 1991. This research was supported
in part by NSF grant DMS89-12362.
2 WILLIAM ARVESON
We discuss some basic issues associated with the problem of modelling quantum
mechanical phenomena on a computer. Before setting out to write code for any