Canonical quantization of classical mechanics in curvilinear coordinates. Invariant quantization procedure

摘要

In the paper is presented an invariant quantization procedure of classicalmechanics on the phase space over flat configuration space. Then, the passageto an operator representation of quantum mechanics in a Hilbert space overconfiguration space is derived. An explicit form of position and momentumoperators as well as their appropriate ordering in arbitrary curvilinearcoordinates is demonstrated. Finally, the extension of presented formalism ontonon-flat case and related ambiguities of the process of quantization arediscussed.