Quantum mechanics in finite dimensions

Abstract

This paper contributes to a recent series discussed quantum mechanics defined on a finite-dimensional Hilbert space in which Weyl's commutations relation for unitary operators holds. In an earlier paper, Santhanam and Teckumalla (1976) showed that the communication relation for hermitian operators with a bounded spectrum tends to Heisenberg's standard cononical commutation relation as the spectrun becomes continuous and the dimension n → ∞ . The present paper offers a formulation which is coordinate free in the limit n → ∞ and makes the limiting procedure especially transparent.