Equivalence of Momentum Operators in Generalized Coordinates

Makoto Kato

J. M. Domingos, Maria Helena Caldeira

Shi-Min Xu, Xing-Lei Xu, Hongqi Li +1 more

Utpal Roy, Suranjana Ghosh, Bhattacharya, Kaushik

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.

Qiao Wen-hua

Correspondence of operator-ih▽ and momentum operator in the quantum mechanics is discussed,and pointed out the simple correspondence in cartesian coordinate does not apply to general curvilinear coordinate,due to Ermi nature of mechanical quantity operator,we can't give corresponding momentum operator directly through simple correspondence under general curvilinear coordinate.

Gary R. Gruber