The first paragraph shows the incompleteness of the formulas proposed by de Broglie for the corpuscular-wave duality (CWD) of a nonrelativistic electron (NE) and in the second paragraph the full CWD of a NE is shown and the deducibility of corpuscular and wave quantities from more general quantities is indicated.
The hundred and fifty years ago, I.Newton, in his corpuscular classic mechanics (CCM), introduced mass as an initial quantity, and, an its basis, defined other corpuscular quantities of CCM. And a hundred years ago, the corpuscular-wave properties of microparticles testified to the inherent corpuscular-wave quantities (CWQ), which as the initial value had the product of mass and wavelength. Accordingly, just as Newton’s CCM was based on corpuscular quantities, corpuscular-wave mechanics (CWM) should have been based on CWQ in the same way. But a hundred years ago, Plank’s and Einstein, to describe the corpuscular-wave properties of the photon, used hybrid of corpuscular quantities Newton’s CCM and wave quantities of wave optics, which a priori, by their definition, were insufficient to describe the CWQ of the photon. Subsequently, de Broglie and Schrödinger applied the method of Planck and Einstein to the case of a non-relativistic electron (NE), and obtained wave quantum mechanics (WQM). But the WQM he obtained turned out to be a real puzzle, and now, a hundred years later, l was able to discover that in reality WQM is an incomplete version of the CWM NE. The campaign managed to find out that Newton’s CCM arises in the form of a special case of the CWM macroscopic body. In this regard, now, l seem to be a Tajikistan physicist who discovered CWQ and CWM physics.
If the statement by Einstein, Podolsky and Rosen on incompleteness of Quantum-Mechanical description of nature is correct, then we can regard Quantum Mechanics as a Method of Indirect Computation. The problem is, whether the theory is incomplete or the nature itself does not allow complete description? And if the first option is correct, how is it possible to complete the Quantum-Mechanical description? Here we try to complement de-Broglie's idea on wave-pilot the stochastic gravitation gives origin to. We assume that de-Broglie's wave-pilots are gravitational stochastic ones, and we shall regard micro-objects as test classical particles being subject to the influence of de-Broglie's waves stochastic gravitation.
Abstract We have seen that it took about two decades to fully realize that light or, generally, electromagnetic radiation has both wave and particle properties. The final proof came with the discovery of the Compton effect (Episode 31). Even Compton himself needed years before he saw that the particle picture of radiation was unavoidable in view of the experimental evidence. Still in the year of Compton’s publications, Louis de Broglie [1] on purely theoretical grounds proposed that the particle–wave duality not only holds for radiation but also for material particles, i.e., for particles with a rest mass such as the electron.
The proposed paper calls attention towards the unobserved mathematical and conceptual inadequacies persisting in the wave-particle duality and matter wave’s concepts, given by Louis de Broglie. Matter wave’s frequency and phase velocity expressions, shown to be inappropriate, are the consequences of these inadequate concepts. The rectifications in these concepts are presented through the corrected implementation of analogy between light waves and matter waves and thus modified frequency and phase velocity expressions are introduced. The proposed expressions are free from all the inadequacies and negations, contrary to that confronted by de Broglie’s proposed expressions. Mathematical proofs for the proposed modified frequency and phase velocity expression are also presented. A novel General Quantum Mechanical Wave Equation is proposed involving the modified phase velocity expression, which itself can precisely derive out Schrodinger’s and Dirac’s Equation.
The irrefutable proof of the incorrectness of the de Broglie hypothesis (postulate) and the Schrödinger equation (postulate) is proposed. The correct methodological basis for the proof is the unity of formal logic and rational dialectics. The unity of formal logic and rational dialectics is the only correct criterion of truth. The proof leads to the following irrefutable conclusion: the de Broglie hypothesis (idea, postulate) and the Schrödinger equation (idea, postulate) are gross errors in mathematics, physics, formal logic and dialectics. This conclusion is based on the following statements: (1) from the point of view of Euler’s formula and the Maclaurin series, the definition of the wave function has neither physical nor mathematical meaning; (2) the substitution of the quantities of energy and momentum, which characterize a quantum (microscopic) particle, into the relationship that describes a macroscopic radiation wave is a gross formal-logical error, because a quantum particle and macroscopic radiation are not identical material objects; (3) in the dialectical and formal-logical points of view, a free classical particle is not identical to a free quantum particle: these particles are non-identical material objects. Therefore, the substitution of the quantities of energy and momentum, characterizing a quantum (microscopic) particle, into the classical relationship that describes the energy and momentum of a classical particle is a gross formal-logical error; (4) in the point of view of formal logic, the concepts of "corpuscular aspect" and "wave aspect" are contradictory (mutually exclusive) concepts. (The concepts of "particle" and "wave" are defined by different essential features of material objects). Therefore, the de Broglie wave function and the Schrödinger wave equation represent a violation of the formal-logical law of lack (absence) of contradiction. This means that the concept of corpuscular-wave dualism is erroneous; (5) The de Broglie wave function and the Schrödinger equation represent a gross dialectical error, because the dimensionless wave function contradicts to the dialectical concept of the measure of a material object (i.e. the dimensionless wave function does not have the qualitative determinacy of a material object, does not characterize the properties of a material object). Therefore, the de Broglie wave function and the Schrödinger equation are meaningless relationships.