The Principle of Commensurability of Conserved Quantities as a Basis for Solving Quantum Mechanics Problems Using Integer Theory - Mykola, Svavil’nyi (Current Research Progress in Physical Science Vol. 7, 2025)
The paper proposes a new method of describing physical reality using the mathematical apparatus of integer theory. Applying this apparatus becomes possible after introducing the principle of commensurability of conserved quantities into physics. It states that at the interaction of physical objects, only such exchanges of conserved quantities (energies, momentums, etc.) are possible so that these quantities have a common measure before and after the interaction of objects. Methods of integer theory solve two classical problems of physics: the radiation spectrum of a hydrogen-like atom and the scattering problem. The known results of such solutions are obtained, and new data are also obtained. It follows from the obtained that the physical reason for the ‘allowed’ states of atomic systems is the necessity of commensurability of the excited states of the atom with its ground state in all conserved quantities. This gives physical foundations to the quantum hypothesis of N. Bohr, which it has not had so far. The strict causal relation between stationary quantum states of atomic systems is also established, i.e. the principle of causality in the quantum world is restored.