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Infinite matrices may violate the associative law

Ofir E. Alon·Nimrod Moiseyev·Asher Peres
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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 $P^2$ is well defined (and diagonal), but its cube $P^3$ is ill defined, because $P P^2\neq P^2 P$. Truncating these matrices to a finite order restores the associative law, but leads to other curious results.

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Ofir E. Alon, Nimrod Moiseyev, Asher Peres. 1998-09-10. Infinite matrices may violate the associative law. https://doi.org/10.1088/0305-4470/28/6/027

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