Infinite matrices may violate the associative law

Details Infinite matrices may violate the associative law Infinite matrices may violate the associative law

1994-12-26

arxiv.org/abs/quant-ph/9412007v2

J.Phys. A28 (1995) 1765-1770

Physics

Quantum Physics

final version in J. Phys. A28 (1995) 1765-1770

Scientific paper

10.1088/0305-4470/28/6/027

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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