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Journal of Physics & Optics Sciences

On Quantum Physics without Schrödinger Equation

Xiao En Wang

Published Apr 25, 2025• 0 citations
Publisher

Abstract

In the early 20th century, Planck, Einstein, Bohr, Sommerfeld, and de Broglie became the pioneers of quantum physics. Because the Schrödinger equation used the wrong energy relationship, it misled people’s understanding of quantum theory. Newtonian mechanics and Leibniz dynamics are correct. But Newton’s first law was tampered with by the British mathematician Mott during his translation, which excluded uniform circular motion from inertia; Leibniz’s kinetic energy mυ2 was modified by French engineer Coriolis to an engineering approximation of mυ2/2. Hamilton mistakenly applied the approximate kinetic energy formula of Coriolis in engineering mechanics to the dynamic analysis in theoretical physics, and established an incorrect Hamiltonian energy equation. Schrödinger ignored Sommerfeld’s research on the constant velocity of electrons in atoms, υ = αc, and thus the constant momentum and constant kinetic energy of electrons. He expressed the constant kinetic energy term of electrons as an operator that hides the velocity variable, and established the wave equation based on the incorrect Hamiltonian energy relationship. The Schrödinger equation deals with the ground state of hydrogen atoms, where electrons die when they reach twice the Bohr radius, which contradicts the stable existence of atoms. The Schrödinger ‎equation has been around for almost a century, and the quantum physics of the new millennium ‎should be a new quantum physics without the Schrödinger equation.

DOI
10.47363/jpsos/icwoq2025/2025(7)5

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In the early 20th century, Planck, Einstein, Bohr, Sommerfeld, and de Broglie became the pioneers of quantum physics. Because the Schrödinger equation used the wrong energy relationship, it misled people’s understanding of quantum theory. Newtonian mechanics and Leibniz dynamics are correct. But Newton’s first law was tampered with by the British mathematician Mott during his translation, which excluded uniform circular motion from inertia; Leibniz’s kinetic energy mυ2 was modified by French engineer Coriolis to an engineering approximation of mυ2/2. Hamilton mistakenly applied the approximate kinetic energy formula of Coriolis in engineering mechanics to the dynamic analysis in theoretical physics, and established an incorrect Hamiltonian energy equation. Schrödinger ignored Sommerfeld’s research on the constant velocity of electrons in atoms, υ = αc, and thus the constant momentum and constant kinetic energy of electrons. He expressed the constant kinetic energy term of electrons as an operator that hides the velocity variable, and established the wave equation based on the incorrect Hamiltonian energy relationship. The Schrödinger equation deals with the ground state of hydrogen atoms, where electrons die when they reach twice the Bohr radius, which contradicts the stable existence of atoms. The Schrödinger ‎equation has been around for almost a century, and the quantum physics of the new millennium ‎should be a new quantum physics without the Schrödinger equation.
Toward the end of the nineteenth century, it became clear that some experiments cannot be explained on the basis of known physics, now referred to as classical physics. In 1900, Max Planck was able to correctly describe the distribution of blackbody radiation energy as a function of wavelength λ or frequency ν = c/λ. He had to accept the existence of energy packets (quanta) with energy E = hν. A few years later, Albert Einstein found that this unexpected relation between energy and frequency is also necessary in order to understand photoemission from metallic surfaces. A decade later, Niels Bohr arrived at the correct equation for the electronic spectrum of the hydrogen atom by applying “quantum conditions” on the motion of the electron around the nucleus and the Planck’s relation E = hν on the energy difference between the energy levels (1916). A decade later, Heisenberg, Born, and Jordan introduced “quantum mechanics” and de Broglie and Schrödinger (1925-1926) introduced “wave mechanics.”
People believe that the Schrödinger equation cannot be used to describe macroscopic objects like the Earth, and Newtonian mechanics cannot be used to describe microscopic systems. The old concept of the relationship between the existing laws of quantum mechanics and classical mechanics undoubtedly has a serious impact on people's understanding of the natural world, the development of physics theories, and the application of existing physics theories. The continuous development of physics theory requires constant changes to some incorrect old concepts. The Schrödinger equation that can describe planetary motion was successfully obtained by replacing the potential energy in the Hamiltonian operator from electromagnetic interaction potential energy to gravitational interaction potential energy. If the distance between the sun and the earth is approximated as a constant, the energy eigenvalues obtained by solving the Schrödinger equation for the Earth's revolution are completely consistent with the results obtained directly using classical mechanics. The direct significance of establishing and applying such equations is that they can simultaneously use classical mechanics and wave dynamics to describe all objects (no longer limited by the mass of the objects), simplifying the calculation process of quantum mechanics. It has been proven that classical mechanics and wave dynamics are compatible, and there is no insurmountable gap between them. This result has a huge positive impact on the theoretical updates and applications of quantum mechanics.
People believe that the Schrödinger equation cannot be used to describe macroscopic objects like the Earth, and Newtonian mechanics cannot be used to describe microscopic systems. The old concept of the relationship between the existing laws of quantum mechanics and classical mechanics undoubtedly has a serious impact on people’s understanding of the natural world, the development of physics theories, and the application of existing physics theories. The continuous development of physics theory requires constant changes to some incorrect old concepts. The Schrödinger equation that can describe planetary motion was successfully obtained by replacing the potential energy in the Hamiltonian operator from electromagnetic interaction potential energy to gravitational interaction potential energy. If the distance between the sun and the earth is approximated as a constant, the energy eigenvalues obtained by solving the Schrödinger equation for the Earth’s revolution are completely consistent with the results obtained directly using classical mechanics. The direct significance of establishing and applying such equations is that they can simultaneously use classical mechanics and wave dynamics to describe all objects (no longer limited by the mass of the objects), simplifying the calculation process of quantum mechanics. It has been proven that classical mechanics and wave dynamics are compatible. It has been proven that classical mechanics and wave dynamics are compatible, and there is no insurmountable gap between them. This result has a huge positive impact on the theoretical updates and applications of quantum mechanics.
Despite its successes, quantum mechanics (QM) has remained mysterious to all who have encountered it. Starting with Bohr and progressing into the present, the departure from intuitive, physical reality has widened. The connection between QM and reality is more than just a “philosophical” issue. It reveals that QM is not a correct or complete theory of the physical world and that inescapable internal inconsistencies and incongruities arise when attempts are made to treat it as physical as opposed to a purely mathematical “tool.” Some of these issues are discussed in a review by F. Laloe [Am. J. Phys. 69, 655 (2001)]. In an attempt to provide some physical insight into atomic problems and starting with the same essential physics as Bohr of e moving in the Coulombic field of the proton and the wave equation as modified by Schrodinger, a classical approach is explored that yields a remarkably accurate model and provides insight into physics on the atomic level. The proverbial view, deeply seated in the wave-particle duality notion, that there is no large-scale physical counterpart to the nature of the electron may not be correct. Physical laws and intuition may be restored when dealing with the wave equation and quantummechanical problems. Specifically, a theory of classical quantum mechanics (CQM) is derived from first principles that successfully applies physical laws on all scales. Rather than using the postulated Schrodinger boundary condition “Ψ → 0 as r → ∞,” which leads to a purely mathematical model of the electron, the constraint is based on experimental observation. Using Maxwell’s equations, the classical wave equation is solved with the constraint that the bound (n = 1)state electron cannot radiate energy. By further application of Maxwell’s equations to electromagnetic and gravitational fields at particle production, the Schwarzschild metric is derived from the classical wave equation, which modifies general relativity to include conservation of spacetime in addition to momentum and matter/energy. The result gives a natural relationship among Maxwell’s equations, special relativity, and general relativity. CQM holds over a scale of spacetime of 85 orders of magnitude — it correctly predicts the nature of the universe from the scale of the quarks to that of the cosmos. A review is given by G. Landvogt [Internat. J. Hydrogen Energy 28, 1155 (2003)].
Replace the potential energy in the Hamiltonian operator from electromagnetic interaction potential energy to gravitational interaction potential energy. Define that the kinetic energy of a moving object is equal to its de Broglie wave's hν. Successfully obtained the Schrödinger equation describing planetary motion. The Schrödinger equation itself is a combination of classical mechanics and quantum mechanics. Quantum mechanics based on it cannot completely exclude classical mechanics. Many examples have been introduced where classical mechanics and quantum theory can be combined to describe the same object (whether it is macroscopic or microscopic). Local realism and determinism still have a market in modern physics. Quantum mechanics and classical mechanics have a compatible and complementary relationship.
Bohr’s theory of the atom was in trouble as soon as it was formulated. Further detailed spectroscopy studies encouraged a proliferation of quantum numbers and ‘selection rules’ in what became known as the Bohr–Sommerfeld model. It couldn’t last, and by 1925 the theory was in crisis. The immediate concern was with the quantum numbers themselves. Where did they come from? Could de Broglie’s hypothesis shed any light? In October 1925 the attentions of Erwin Schrödinger were drawn to a footnote in one of Einstein’s recent papers. Intrigued, Schrödinger acquired a copy of de Broglie’s PhD thesis. Although he eventually published a more obscure derivation, Schrödinger essentially applied the de Broglie relation to the classical equation of wave motion. He applied the result to the hydrogen atom, and showed that the quantum numbers emerge ‘in the same natural way as the integers specifying the number of nodes in a vibrating string’.