Unusual commutation relations in physics
(2010) American Journal of Physics — Vol. 78, n° 12, p. 1365 (2010)
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- Abstract
- The angular momentum operator math of a particle obeys the usual commutation rule math×math = iℏmath. In contrast, the total angular momentum operator math of a set of particles relative to moving axes (as, for instance, when mounted on a tumbling molecule) obeys the anomalous commutation rule math×math = −iℏmath. We give a pedagogical and mathematically nonsophisticated description of intermediate cases for which partial angular momentum operators, relative to various moving frames, obey unusual commutation relations that are neither usual nor anomalous. Insight into the origin of these unusual commutation relations provides a means of guessing the type of commutation rule that will be obeyed. In particular, it gives a way to avoid, as far as possible, the unusual commutation relations, which lead to complicated and nonsystematic expressions. Some examples from molecular physics are presented.
- Affiliations
Université de Montpellier II CTMM, Institut Charles Gerhardt
Citations
Nauts, A., & Gatti, F. (2010). Unusual commutation relations in physics. American Journal of Physics, 78(12), 1365. https://doi.org/10.1119/1.3482257 (Original work published 2010)