Canonical quantization of classical mechanics in curvilinear coordinates. Invariant quantization procedure
2013
scientific article
english
- quantum mechanics
- deformation quantization
- canonical transformations
- moyal product
- phase space
EN In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over configuration space is derived. An explicit form of position and momentum operators as well as their appropriate ordering in arbitrary curvilinear coordinates is demonstrated. Finally, the extension of presented formalism onto non-flat case and related ambiguities of the process of quantization are discussed.
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