Infinite matrices may violate the associative law
O E Alon; N Moiseyev; A Peres; O E Alon; Dept. of Chem., Technion-Israel Inst. of Technol., Haifa, Israel; N Moiseyev; Dept. of Chem., Technion-Israel Inst. of Technol., Haifa, Israel; A Peres; Dept. of Chem., Technion-Israel Inst. of Technol., Haifa, Israel
Журнал:
Journal of Physics A: Mathematical and General
Дата:
1995-03-23
Аннотация:
The momentum operator for a particle in a box is represented by an infinite-order Hermitian matrix P. Its square P<sup>2</sup> is well-defined (and diagonal), but its cube P<sup>3</sup> is ill-defined, because P P<sup>2</sup> not=P<sup>2</sup> P. Truncating these matrices to a finite order restores the associative law, but leads to other curious results.
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