arXiv:quant-ph/9412007 · Journal of Physics A Mathematical and General

Infinite matrices may violate the associative law

Ofir E. Alon, Nimrod Moiseyev, Asher Peres

Published Mar 23, 1995• 4 citations

Abstract

The momentum operator for a particle in a box is represented by an infinite-order Hermitian matrix P. Its square P 2 is well-defined (and diagonal), but its cube P 3 is ill-defined, because P P 2 not=P 2 P. Truncating these matrices to a finite order restores the associative law, but leads to other curious results.

DOI: 10.1088/0305-4470/28/6/027

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