Infinite matrices may violate the associative law

O. E. Alon; N. Moiseyev; A. Peres

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

Infinite matrices may violate the associative law

O. E. Alon, N. Moiseyev, A. Peres

Research output: Contribution to journal › Article › peer-review

Abstract

The momentum operator for a particle in a box is represented by an infinite-order Hermitian matrix P. Its square P² is well-defined (and diagonal), but its cube P³ is ill-defined, because P P² not=P² P. Truncating these matrices to a finite order restores the associative law, but leads to other curious results.

Original language	English
Article number	027
Pages (from-to)	1765-1769
Number of pages	5
Journal	Journal of Physics A: Mathematical and General
Volume	28
Issue number	6
DOIs	https://doi.org/10.1088/0305-4470/28/6/027
State	Published - 1995
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy

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10.1088/0305-4470/28/6/027

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abstract = "The momentum operator for a particle in a box is represented by an infinite-order Hermitian matrix P. Its square P2 is well-defined (and diagonal), but its cube P3 is ill-defined, because P P2 not=P2 P. Truncating these matrices to a finite order restores the associative law, but leads to other curious results.",

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AB - The momentum operator for a particle in a box is represented by an infinite-order Hermitian matrix P. Its square P2 is well-defined (and diagonal), but its cube P3 is ill-defined, because P P2 not=P2 P. Truncating these matrices to a finite order restores the associative law, but leads to other curious results.

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Infinite matrices may violate the associative law

Abstract

ASJC Scopus subject areas

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