1998/12/31 by E. A. Tagirov
Physics and Astronomy · #gr-qc
published as Grav.Cosmol. 5 (1999) 23-30 · 15 pages, LaTex 2.09-file, submitted to "Gravitation and Cosmology". Revised in January 06.99 version: addition improving the end of Sec.4 and a correction of the formula (38) of the initial text (the formula (40) in the present text)
arxiv created 1999/01/11 · arxiv updated 2009/11/30
This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the 1+3-formalism is considered, the result of which will be compared in the subsequent paper II with that of the field-theoretical approach, see also gr-qc/9807030. The Schrödinger representation of quantum-mechanical kinematics and dynamics is presented in the general-covariant form and a physical interpretation of the state vectors and the position operators is discussed.