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The ubiquitous XP commutator

A. C. de la Torre
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Abstract

Position and momentum of a particle can take any value in a continuous spectrum; these values are independent but their indeterminacies are correlated; momentum and position are mutually the generators of the transformations in each other. It is shown in a concise way, how all these features arise solely from their commutation relation $[X,P]=i\hbar$. The article is complete and self contained, adequate for didactic use.

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A. C. de la Torre. 2005-09-23. The ubiquitous XP commutator. https://doi.org/10.1088/0143-0807%2F27%2F2%2F005

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