Quantum mechanical ordering problem for observables which are linear in momentum
- 1 December 1975
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 8 (12) , 1863-1867
- https://doi.org/10.1088/0305-4470/8/12/004
Abstract
Starting with Segal's postulates (1960) for quantum mechanics, augmented by the postulate that the commutators of the free Hamiltonian with position observables are canonical, the authors prove that the quantum mechanical observable Q(X), which corresponds to the function C(X) identical to Xi(q)pi on phase space in classical mechanics, is equal to the anticommutator 1/2(Q(Xi),Q(pi)). In coordinate free language, this means the Q( phi X)=1/2(Q( phi ),Q(X)) for any scalar field phi and any vector field X on the configuration space.Keywords
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