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.
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.
This paper derives the non-relativistic time-dependent Schrödinger equation as the logically unavoidable dynamical law for de Broglie matter waves, extending the reconstruction begun in the companion work “The Logical Origin of the de Broglie Matter Wave and its Physical Meaning (the Born Rule)” (Chan, 2026). Starting from the same minimal premises—continuous position in real space, Fourier conjugacy (and the logical uncertainty principle), translation invariance via Noether’s theorem, and probability conservation via statistical energy flux—the Schrödinger equation follows deductively once norm preservation and classical non-relativistic correspondence are enforced. The derivation proceeds in clear stages: Plane-wave solutions for free particles and constant potentials, Quadratic dispersion relation from classical kinematics, Exact local plane-wave structure (defined via phase gradients) that must hold at every point for any smooth wave function, The unique linear differential operator of order ≤ 2 that consistently “glues” these local structures across smooth external potentials V(x,t) while preserving the L²-norm (unitarity). No canonical quantization, operator promotion, commutation relations, or postulated wave equations are used. The Born rule is taken as already established from the prior paper and serves only to constrain unitary evolution. The Schrödinger equation thus emerges not as an empirical postulate or convenient ansatz, but as the mathematically and symmetrically forced description of indivisible particles propagating in continuous, translationally invariant (or smoothly perturbed) space. Domain of validity and natural limitations (non-relativistic kinematics, smooth potentials, single-particle/mean-field regime, closed-system unitarity) are explicitly delineated.
The correct critical analysis of the generally accepted foundations of quantum mechanics is proposed [1]. The purpose of the analysis is to prove that the foundations include logical errors. The principle of the unity of formal logic and dialectics is a methodological basis of the analysis. The result is as follows: (a) the generally accepted foundations (i.e., the interpretation of the experimental data on diffraction of quantum particles; the conception of wave-corpuscle dualism; the probabilistic interpretation of the psi-function) are logical errors; (b) the pseudo-informational meaning is the true meaning of the psi-function. Conclusion is that quantum mechanics is not a physical, objective theory but a pseudo-informational one. Therefore, quantum mechanics should be replaced by a physical, objective quantum theory.
Physics is also known as a science of observation and experiment. In this paper, the most representative experimental verification of general relativity, "Mercury perihelion precession", is used for mathematical derivation and analysis, and the serious errors in the experimental verification are expounded deeply. Furthermo2re, the Lorentz transformation, the core formula of special relativity, is mathematically deduced and analyzed, and the contradictions and errors existing in the Lorentz transformation are profoundly revealed. These contradictions and errors involve the deep relationship between physics and mathematics, and are also the core problems faced by theoretical physics. Minkowski's four-dimensional spacetime contradicts the "principle of constant speed of light", and there are serious errors in the "relativity of simultaneity". The so-called experimental verification of the theory of relativity is false, and there is a fundamental error in the theory of relativity, which will lead to the collapse of the whole theoretical building, including general relativity. The basic formula of quantum mechanics, "matter wave" wavelength λ=h/p , is also based on the wrong Einstein "massenergy equation". Therefore, the wave function of "matter wave" established on the wavelength λ=h/p of "de Broglie wave" and the Schrodinger equation are all pseudo-formulas without any physical significance. Schrodinger equation is the core formula of quantum mechanics. This is enough to cause the collapse of quantum mechanics.The mathematical derivation of the Compton effect was completely based on the pseudo-concepts of special relativity such as "mass-energy equation" and "moving mass", while Einstein's explanation of the photoelectric effect was limited by the scientific and technological level at that time. The Compton effect and the photoelectric effect, as the two most important experimental verification of the "waver-particle duality" of light, were not valid. "Wade-particle duality" is another misdirection of Einstein to human beings, which "inspired" de Broglie to put forward the famous "matter wave" hypothesis, and the "matter wave" concept is the root that led theoretical physics to fall into the abyss of quantum mechanics. In addition, there are serious errors in the basic concept of quantum mechanics. "Monochromatic radiant outdegree" is an incomplete definition of physics, which is also the root cause of the "ultraviolet disaster" problem. The defective physics concept of "monochromatic radiant outdegree" is also an important reason for theoretical physics to fall into the "quantization" quake-pit. The "ultraviolet catastrophe" problem of blackbody radiation is a physical accident caused by the artificially defined defect concept of "monochromatic radiance outdegree". Boer's hydrogen atom theory is the foundation theory of quantum mechanics. Like relativity theory, this theory also has the problem that the same mathematical symbol expresses two contradictory physical meanings at the same time. Quantum tunneling has the problem of different physical interpretation of mathematical formulas. No matter the premise or the core formula, there are serious contradictions and errors in quantum mechanics, and quantum mechanics is also a wrong theory. The theory of relativity and quantum mechanics is a lost on the journey of human truth exploration. The fundamental errors of relativity and quantum mechanics will lead to the comprehensive collapse of theoretical physics system including relativistic quantum mechanics, quantum field theory (quantum electrodynamics, quantum chromodynamics, unified theory of weak electricity, standard model of elementary particle physics), Yang Mills theory and so on. Fortunately, in the course of nearly a century of exploration, human beings have accumulated a large number of empirical results. Although the theory Journal of Electrical Electronics Engineering ISSN: 2834-4928 1 Department of Mathematical Science, College of Science, Tsinghua University, Beijing 100084, China 2 School of Physics, Peking University, Beijing 100091, China 3 School of Astronomy and Space Science, University of Science and Technology of China, Anhui 230026, China J Electrical Electron Eng, 2023 Volume 2 | Issue 4 | 381 of relativity is completely wrong, it does not affect the real existence of such an objective thing as the atomic bomb. Laser, transistor, tunnel microscope and so on have nothing to do with quantum mechanics, because quantum mechanics is also a fundamentally wrong theory, but this does not hinder the validity of the existing experimental results, the so-called experimental verification of relativity and quantum mechanics are forced to incorporate experimental results and physical phenomena into their own theoretical system. Special thanks to Academician Chen Jia-er for his theoretical guidance and help
The Einstein relationship, the de Broglie relationship, and the Born rule are considered fundamental in quantum mechanics, yet in mathematical logic, as usually written, they are not self-consistent [1]. On the other hand, each has had great success individually at predicting the outcome of experiments. It is shown here that the lack of self-consistency can be remedied if it is assumed the wave is physical, and the equation for the wave, and not the particle, is actually the Schrödinger equation.
The Schrödinger equation was really postulated rather than derived. But we can see why it was postulated. It has been proven to be valid, in that it provides information about small, slow moving particles subject to a wide variety of potentials. The derivation of the time-dependent Schrödinger equation (TDSE) follows rather directly from assuming a free particle wave: Ψ = e i(kx-ωt) . If this wave function is plugged into the classical wave equation, and quantum principles are used, the two sides of the equation are not equal (this means this function does not "solve" the equation). The quantum principles required are an understanding of the photoelectric effect (by which E = ħω) and the de Broglie hypothesis (λ = h/p). Using these relationships, we show that one derivative of time is equal to a double derivative with respect to position, with a few proportionality factors mixed in. Thus, the TDSE for a free particle is just a statement that kinetic energy equals total energy . For a non-free particle (subject to a potential), potential must merely be added to the left-hand side of the equation, to yield kinetic energy plus potential energy equals total energy .
This paper analyzes the quantities of energy and momentum in the definitional rela-tionship of relativistic mechanics, in the de Broglie momentum hypothesis and in the Klein-Gordon, Dirac and Schrodinger equation. The results of analysis shows that Planck constant and relativistic relationships on the length contraction and increase in mass are a reflection of the same physical principles in nature, that λ designated in the de Broglie hypothesis λ =h/mv as the wave of matter with rest state value λ = ∞ must be connected with a real dimension of a particle with rest state value λ = lo = moc and that on this ba-sis we can come to the fundamental equations of quantum mechanics that are the Klein-Gordon, Dirac and Schrodinger equation without the necessity of the wave functions.