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Schrödinger’s wave quantum mechanics is actually the corpuscular-wave mechanics of a non-relativistic electron.

Субхон Джомирзоев

Published Feb 7, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.24108/preprints-3113382

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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.
In its physical meaning, Planck’s constant turned out to be one of the corpuscular-wave quantities (CWQ) of microparticles. In turn, the newly discovered CWQ turned out to be quantities of corpuscular-wave mechanics (CWM), just as corpuscular quantities are quantities of the Newton’s corpuscular classical mechanics (CCM). At the same time, Schrödinger’s wave quantum mechanics (WQM) turned out to be in fact incomplete part of the CWM of non-relativistic electron (NE), and Newton's CCM itself turned out to be derived from the CWM macroscopic body (MB). Thus, to our great surprise, the CWM of a NE turned out to be more general form of Schrödinger’s WQM, and the CWM of a MB turned out to be more general form of Newton’s CCM. In this regard, just Abel discovered the multiplicity of algebras, and Lobachevsky discovered the multiplicity of geometries, similar to them, we encountered the multiplicity of the mechanics of physics.
Newtonian mechanics is the foundation of Classical Physics. Newton’s mechanics, Thermodynamics, Wave theory of Optics and Maxwell’s electromagnetic theory belong to regime of Classical Physics and can be used to explain a wide range of phenomena in the Universe at macroscopic scale. These theories fail spectacularly when applied to phenomenain the atomic and nuclear regime, for example, proton-atom scattering or the flow of electrons in a semiconductor. Quantum mechanics is the most successful scientific theory that has ever been created and it has completely changed our view of the world. The failure of Classical Physics was highlighted by black body radiation and photoelectric effect. Max Planck and Albert Einstein provided explanations of both phenomena based on quantum hypothesis and are thus considered founders of Quantum Physics. The origin of quantum mechanics goes back to the mid-1920s.It was formulated first as matrix mechanics by Werner Heisenberg, Max Born and Pascual Jordan; then as wave mechanics by Louis de Broglie and Erwin Schrödinger; and later on asquantum statistics of subatomic particles by Fermi-Dirac and Bose-Einstein. Combining relativistic mechanics with quantum mechanics, Dirac formulated his relativistic quantum mechanics during 1930s. Uncertainty Principle is thecornerstone of Quantum Physics. The role of randomness in microscopic physical processes shatters the myth that the universe is deterministic. Quantum world is unpredictable in the classical sense and demolishes the idea of an objective universe. The Copenhagen interpretation remains the quantum mechanical formalism that is currently most widely accepted amongst physicists.Quantum theories support cosmic spirit pervading the cosmos and inter – relationship of individuals in the world society. Quantum philosophy is holistic and is going to revolutionize our world-view.
Elements of quantum mechanics Quantum mechanics was discovered in 1925 through groping efforts to compromise two apparently contradictory pictures on the fundamental entities in nature. One was the wave picture for light which was later extended to matter by de Broglie, another was the corpuscular picture of matter which was later extended to light by Einstein. Schrödinger's wave equation came as a natural development of the first stream, while Heisenberg's matrix mechanics was presented as a unique proposal from the second stream. In spite of completely different appearances, the two theories proved, within a couple of years after their discoveries, to be equivalent. This is a most beautiful example that the physical reality exists independent of the mathematical framework formulated for its description. In this chapter, we will give a very brief review of the principles of quantum mechanics, 1–3 mainly with the harmonic oscillator as a model system for the following reasons. The first is historical: the electromagnetic wave, whose interaction with matter is the subject of this book, is a harmonic oscillator, a system which was for the first time subject to “quantization”, thus opening a way to the discovery of quantum mechanics. The second is technical: the harmonic oscillator is one of very few examples of analytically soluble problems in quantum mechanics. The third is pedagogical: the harmonic oscillator is a system best suited for realization of the equivalence of the two different pictures mentioned above and hence for a deeper understanding of the principles of quantum mechanics.
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.”
Some two centuries before the quantum revolution, Newton (1) suggested that corpuscles of light generate waves in an aethereal medium like skipping stones generate waves in water, with their motion then being affected by these aether waves. Times have changed. Light corpuscles are now known as photons, and the majority of physicists have dispensed with the notion of aether. Nevertheless, certain features of Newton's metaphor live on in one particular version of quantum mechanics. According to pilot wave theory, first proposed by de Broglie (2) and later developed by Bohm (3) with Einstein's encouragement, microscopic elements such as photons and electrons consist of both particle and wave, the former being guided by the latter. Although this physical picture has not been widely accepted, it has had some notable proponents, including Bell (4). Its principal appeal is that it restores realism and determinism to quantum mechanics, its weakness that the physical nature of the guiding wave field remains unclear. At the time that pilot wave theory was developed and then overtaken by the Copenhagen interpretation as the standard view of quantum mechanics, there was no macroscopic pilot wave analog to draw upon. Now there is.