Quantization in curvilinear coordinates

Abstract

Two prescriptions often used to find Hermitian operators corresponding to classical quantities can be removed. Components of momentum are of three types, linear momentumP〈q〉k canonical momentumP(q)k and generalized momentumPqk. Using metrical geometry, their mutual relations are established. The operatorsP〈q〉k andP(q)k are given by substituting quantum commutation brackets for classical Poisson brackets. The relations among classical quantities are divided into two types according to whether they have physical meaning. Those which have physical meaning go over into the corresponding operator relations.