A general approach to the description of an angle and phase is given on the basis of the $\mathrm{kq}$ representation. It is shown that an angular coordinate in quantum mechanics has to be treated as a quasicoordinate in order to avoid inconsistencies. The $\mathrm{kq}$ representation leads to a consistent definition of the angular-momentum-angle degree of freedom. Using the correspondence between classical and quantum mechanics for the phase of a harmonic oscillator, operators are defined that form a new quantum-mechanical representation. This representation clarifies the concept of the phase and sheds light on the general understanding of rotations in quantum mechanics.A general approach to the description of an angle and phase is given on the basis of the $\mathrm{kq}$ representation. It is shown that an angular coordinate in quantum mechanics has to be treated as a quasicoordinate in order to avoid inconsistencies. The $\mathrm{kq}$ representation leads to a consistent definition of the angular-momentum-angle degree of freedom. Using the correspondence between classical and quantum mechanics for the phase of a harmonic oscillator, operators are defined that form a new quantum-mechanical representation. This representation clarifies the concept of the phase and sheds light on the general understanding of rotations in quantum mechanics.

Physical ReviewNov 25, 196930 citations

Representation in Quantum Mechanics

Richard Healey

Elsevier eBooksJan 1, 20260 citations

Quantum Mechanics as a Classical Theory X: Quantization in Generalized Coordinates

L. S. F. Olavo

In this tenth paper of the series we aim at showing that our formalism, using the Wigner-Moyal Infinitesimal Transformation together with classical mechanics, endows us with the ways to quantize a system in any coordinate representation we wish. This result is necessary if one even think about making general relativistic extensions of the quantum formalism. Besides, physics shall not be dependent on the specific representation we use and this result is necessary to make quantum theory consistent and complete.In this tenth paper of the series we aim at showing that our formalism, using the Wigner-Moyal Infinitesimal Transformation together with classical mechanics, endows us with the ways to quantize a system in any coordinate representation we wish. This result is necessary if one even think about making general relativistic extensions of the quantum formalism. Besides, physics shall not be dependent on the specific representation we use and this result is necessary to make quantum theory consistent and complete.

arXiv:quant-ph/9601002Jan 3, 19960 citations

Representations of Quantum Mechanics

John C. Inkson

Springer eBooksJan 1, 19840 citations

On Quantum Mechanical Operators in Generalized Coordinates

Gary R. Gruber

American Journal of PhysicsOct 1, 19725 citations

A general approach to the description of an angle and phase is given on the basis of the

\mathrm{kq}

representation. It is shown that an angular coordinate in quantum mechanics has to be treated as a quasicoordinate in order to avoid inconsistencies. The

\mathrm{kq}

representation leads to a consistent definition of the angular-momentum-angle degree of freedom. Using the correspondence between classical and quantum mechanics for the phase of a harmonic oscillator, operators are defined that form a new quantum-mechanical representation. This representation clarifies the concept of the phase and sheds light on the general understanding of rotations in quantum mechanics.