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This document presents a strengthened canonical quantization scheme for a particle constrained on a curved hypersurface, introducing a second category of fundamental commutation relations. It derives the geometric momentum and resolves a long-standing issue regarding the geometric potential for a particle on a spherical surface, concluding that the geometric potential is determined by the mean curvature. The findings emphasize the importance of Cartesian coordinates in the quantization process and provide a

Author

Muhammad Ramzan

Language

EN