Some intricacies of the momentum operator in quantum mechanics

Details Some intricacies of the momentum operator in quantum mechanics Some intricacies of the momentum operator in quantum mechanics

2007-06-06

arxiv.org/abs/0706.0924v2

Physics

Quantum Physics

Minor corrections included. 9 pages, latex file. To be published in Revista Mexicana de Fisica

Scientific paper

In quantum mechanics textbooks the momentum operator is defined in the Cartesian coordinates and rarely the form of the momentum operator in spherical polar coordinates is discussed. Consequently one always generalizes the Cartesian prescription to other coordinates and falls in a trap. In this work we introduce the difficulties one faces when the question of the momentum operator in general curvilinear coordinates arises. We have tried to elucidate the points related to the definition of the momentum operator taking spherical polar coordinates as our specimen coordinate system and proposed an elementary method in which we can ascertain the form of the momentum operator in general coordinate systems.

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