Methodological requirements and some basic issues of quantum mechanics

Waves and particles are alternative modes of being for the elements of atomic dimensions. This feature appears to be evident at the experimental level but remains a conundrum at the theoretical level. The squared wavefunction vertical bar Psi vertical bar 2 yields the probability of finding a particle at a particular position and time, namely, the wave is conceived as a derivation or a physical condition of the particle and not a condition of the quantum. What the wavefunction represents, whether it really exists, whether it is a purely formal representation and if the observer influences the wavefunction are the major arguments of quantum mechanics (QM). The double nature of electrons, photons, and so on has been clearly recognized, and the two natures should be established by precise formulations. This work adheres totally to this methodological criterion and puts forward two formal definitions. The measurement process and wave collapse problems are also discussed. Finally, we verify the theoretical conclusions using the double slit experiment and the photoelectric effect. Probability plays a crucial role in the quantum literature, and the definitions of the wave and the particle should be illustrated by exploiting the probability theory; however, the various probability theories are not univocal and propose irreconcilable views. Therefore, in a preliminary stage, we have unified the ontological and epistemic interpretations of probability. Four theorems, already published, are used here. In summary, this work is developed on the basis of two methodological criteria, which require to improve the probability theory and to fix the definitional formulas of QM. (C) 2022 Physics Essays Publication.