The wave equations for oscillator with Planck's constant and with a quantum of force

• Published in: Physics and chemistry of the earth. Part A, Solid earth and geodesy Solid earth and geodesy, 1999, Vol.24 (8), p.721-725
• Main Author: Malimon, A.N.
• Format: Article
• Language: English
• ISSN: 1464-1895
• DOI: 10.1016/S1464-1895(99)00105-2

The model of oscillator with mass m is considered. The expression for potential energy of oscillator U = mω2x2/2 is symmetric with respect to angular frequency ω and coordinate x. Provided that in case of small ω not the mechanical angular momentum mωx2, but the force mω2x is quantizied, a wave equation of mass motion is examined. This wave equation contains a quantum of force and is examined in ω-space. Such an equation is similar to the Schrodinger equation for harmonic oscillator with Planck's constant in x-space. The wave equation with quantum of force gives the spectrum of values of oscillator energies En = Hx(n+1/2), where H is the quantum of force, n = 0,1,2,…. Theoretical estimate for gravitation force quantum H is 10−37 ÷ 10−36 N. A few results of observational cosmology can be explained by quantization of force. The model presented permits one to link directly the Newton's laws of classical mechanics and the quantum theory. Moreover, such an approach allows one to explain the frequency steps of quantum standards and also irregular globally-correlated frequency variations of standards.