To Principles of Quantum Mechanics Development

TL;DR

This paper offers new insights into the foundational principles of quantum mechanics, emphasizing the importance of the second main postulate and its formulation, and discusses potential directions for its development based on a clearer understanding of wave-particle duality.

Contribution

It provides a rigorous formulation of the second main postulate in quantum mechanics, grounded in electromagnetic field theory, and analyzes its implications for the development of quantum theory.

Findings

The second main postulate can be strictly formulated as a statement.

The Schrödinger formulation of the postulate is mathematically rigorous.

The probabilistic interpretation by Born is valid only in specific cases.

Abstract

New insight to the principles of the quantum physics development is given. The correct ways for the construction of new versions of quantum mechanics on the second main postulate base are discussed. The conclusion on the status of the second main postulate is given. Its formulation in all textbooks has to be represented in the form of statement, since the hypothesis of Schr\"odinger on the existance of the field scalar function, being to be observable quantity, just charge density, is strictly proved for the case of EM-field, the role of which is argued to be decisive for the dynamics of the atomic systems. It is shown, that the field scalar function, being to be the function the only of coordinates and time, actually describes the state of the system. The second main postulate in Schr\"odinger formulation is mathematically strictly grounded, but in the popular probabilistic form used in modern textbooks on quantum theory it cannot be proved. The probabilistic theatise, proposed by Born is true in a number of special cases, quite correctly indicated by Dirac. The possible ways of the development of quantum theory, based on clear understanding of the origin of corpuscular-wave dualism are analysed.