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On the Momentum Operator in Polar Coordinates

Feng Wen-Lin

By using the relation between polar coordinates and cartesian descartes coordinates and the method of symmetry,and with the consideration of the course of construction and the hermicity and commutability of operators,the components of momentum operator in polar coordinates are constructed as:pρ-ih(/ρ+1/2ρ),pφ=-i-h/ρ.

Journal of Yibin UniversityJan 1, 20110 citations

About the Choice of Momentum Operator Under Coordinate Representation

Liu Han-kui

This article discusses in detail about the presentation of the momentum operator P under coordinate representation. The result indicates that it is not the only way to choose P=-ih (?) in common sense for simple-ness,And it has more general significance to define coordinate operator X and momentum operator P by using the canonical commutation rule of [X,P]=ih.

Jan 1, 20040 citations

The components of relativistic momentum don't include the item of Σ_z in spherical coordinate system

Kun Hu

The matrix forms of the components α_r,α_θ and α_φ of the vactor α in spherical coordinate system in dirac relativistic quantium mechanics are given,and the operational character among these matrixes is given too.The commutation relations between the momentun differential 0 operators ρ_r,ρ_θ and ρ_φ and α_r,α_θ and α_φ,and the unit vectors e_r,e_θ and e_φ are given,further the expressions of relativistic momentum components in spherical coordinate system are given.

Jan 1, 20040 citations

Some intricacies of the momentum operator in quantum mechanics

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.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.

arXiv:0706.0924Jun 6, 20074 citations

Quantum operators in generalized coordinates

Pedro Villaseñor-González, Joel Uriel Cisneros-Parra

It will be shown in this paper how to build quantum operators in generalized coordinates. A direct substitution of momentum operators in the classical expression suffices; the only condition being that this expression must be written in matrix form before the substitution. Specifically, we are then able to show that the two operators −ih/(∂/∂Q) and −ih/g−1/2 (∂/∂Q)g1/2, and only these, are to be associated with generalized momenta.

American Journal of PhysicsAug 1, 198116 citations

Different Coordinate Momentum Operator

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.

Yinshan Academic JournalJan 1, 20110 citations

Momentum Operater in a Spherical Coordinates Serie

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Momentum Operater in a Spherical Coordinates Serie

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