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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy (all)