Infinite matrices may violate the associative law
Ofir E. Alon, Nimrod Moiseyev, Asher Peres
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≠ P2 P. Truncating these matrices to a finite order restores the associative law, but leads to other curious results.
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