A.N. Malimon

FSUE “VNIIFTRI”, Mendeleevo, Moscow region
amalimon@vniiftri.ru

Al’manac of Modern Metrology № 1 (21) 2020, pages 50–64

In this article author analyzes the ways of giving the Newtonian law of gravitation a mathematical form corresponding to the assumption of the quantum nature of the gravitational force. Theoretical models of two types of quantum oscillators are considered, for one of which the energy spectrum is directly proportional, and for the other it is inversely proportional to the distance between gravitating masses. Author proposes Schrödinger-type wave equation to describe in quan-tum language the bound motion of a test body m in a field of large mass M. In this equation the gravitational action parameter plays the role of the Planck’s constant. The solutions of this equation determine the radius of the orbits r_n of the test body and the spectrum of energy levels E_n. A quantum expression is obtained for the Newtonian gravitational force acting on the test mass m. This expression corresponds to its classical value.

Key words: quantization in a gravitationally bound planetary system, Schrödinger equation with gravitational action parameter, dual wave mechanics.

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