Quantization and independent coordinates

Abstract

This paper reviews canonical and other quantization methods, gives a quantization rule that gives results that agree with those obtained by direct transformation of the Laplacian, and thus expresses the correct Hamiltonian operator in terms of proper conjugate momentum operators. It gives applications to a number of curvilinear coordinates, introduces the class of independent coordinates, presents generalized Jacobi coordinates, and discusses the molecular vibration-rotation Hamiltonian.