Quantum mechanics in Riemannian spacetime. II. Operators of observables

The formulation of the generally covariant analog of standard (nonrelativistic) quantum mechanics in a general Riemannian spacetime begun in earlier studies of the author is continued with the introduction of asymptotic (with respect toc^‑2) operators of the spatial position of a spinless particle and of the projection of its momentum onto an arbitrary spacetime direction. The connection between the position operator and the generalization of theV_1,3 Newton—Wigner operator is established. It is shown that the projection of the momentum onto the 4-velocity of the frame of reference (the energy operator) is unitarily equivalent to the Hamiltonian in the Schrödinger equation.