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Global Journal of Human Social Science

Quantization Essence

Stanislav Ordin

Published Jul 28, 2023• 0 citations
Publisher

Abstract

Ideal Resonance does not fade, and thus, it is, as it were, out of time. So the corresponding Planck QUANTUM, which determines the STATIONARY Allowed States of Energy, is simply a reflection of the Ideal Resonance. which "Quantum Mechanics" used on the example of the Mechanical Harmonic Oscillator. And the fundamental difference of QUANTUMS is only that for frequencies not equal to zero and their minimum energy of the Resonance-Quantum has a finite, non-zero initial value, which also determines the minimum distance between the allowed energy levels. At the same time, the internal structure of the QUANTUM can be not only electromagnetic, like Planck's, and not only acoustic, like Einstein's, but also be determined by the so-called de Broglie matter waves. But, in order to remove any mysticism from QUANTUMS, one must UNDERSTAND that the DUALISM introduced by them is determined by Pontryagin's functional connection of the ELEMENTARY PARTICLE and the Packet of Waves that form it.

DOI
10.34257/gjsfravol23is5pg21

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Ideal Resonance does not fade, and thus, it is, as it were, out of time. So the corresponding Planck QUANTUM, which determines the STATIONARY Allowed States of Energy, is simply a reflection of the Ideal Resonance. which "Quantum Mechanics" used on the example of the Mechanical Harmonic Oscillator. And the fundamental difference of QUANTUMS is only that for frequencies not equal to zero and their minimum energy of the Resonance-Quantum has a finite, non-zero initial value, which also determines the minimum distance between the allowed energy levels. At the same time, the internal structure of the QUANTUM can be not only electromagnetic, like Planck's, and not only acoustic, like Einstein's, but also be determined by the so-called de Broglie matter waves. But, in order to remove any mysticism from QUANTUMS, one must UNDERSTAND that the DUALISM introduced by them is determined by Pontryagin's functional connection of the ELEMENTARY PARTICLE and the Packet of Waves that form it.
Ideal resonance does not fade, and thus, it is, as it were, out of time. Therefore, the corresponding Planck QUANTUM, which determines the STATIONARY allowed states of energy, is simply a reflection of the ideal resonance. So the corresponding Planck QUANTUM, which determines the STATIONARY Allowed States of Energy, is simply a reflection of the Ideal Resonance. And modern “Quantum Mechanics,” which moved away from both Planck’s Quantization and the correct use of the Mechanical Model, simply used a simplified analysis of the Mechanical Harmonic Oscillator. The fundamental difference of QUANTUMS is only that for frequencies not equal to zero and their minimum energy of the resonance-quantum has a finite, non-zero initial value, which also determines the minimum distance between the allowed energy levels. At the same time, the internal structure of the QUANTUM can not only be electromagnetic, like Planck’s, and not only be acoustic, like Einstein’s, but also be determined by the so-called de Broglie matter waves. However, in order to remove any mysticism from QUANTUMS, one must UNDERSTAND that the DUALISM introduced by them is determined by Pontryagin’s functional connection of the ELEMENTARY PARTICLE and the packet of waves that form it.
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.
This chapter presents the origins of quantum mechanics. The story of how people hit on the highly non-intuitive world picture of quantum mechanics, in which the physical state of a system is represented by an element in an abstract linear space and its observable properties by operators in the space, is fascinating and exceedingly complicated. The much greater change from the classical world picture of Newtonian mechanics and general relativity to the quantum world picture came in many steps taken by many people, often against the better judgment of participants. There are three major elements in the story. The first is the experimental evidence that the energy of an isolated system can only assume special discrete or quantized values. The second is the idea that the energy is proportional to the frequency of a wave function associated with the system. The third is the connection between the de Broglie relation and energy quantization through the mathematical result that a wave equation with fixed boundary conditions allows only discrete quantized values of the frequency of oscillation of the wave function (as in the fundamental and harmonics of the vibration of a violin string).
Schrödinger's "searchlight" made it possible to enlighten the atom and cast shadows on the "Screen of the Observer". But the main trouble of the modern "Quantum Theory" is precisely that it mistook the shadows from the "Elephant" for the "Elephant" itself, for Reality. This led to a catastrophic discrepancy between the allowed calculated energy levels of electrons and the experimental ionization potentials with an increase in the mass of atoms. But the inclusion of "normal illumination" - understanding gives a real Quantum Theory, which can be built on the path laid by Planck-de Broglie-Einstein-Heisenberg-Bohm. Quantization adds a new invariant and strictly mathematically, according to Planck, expands complements the Classics, and does not deny it - Resonant orbits of electrons in atoms - Electronic Orbitals correspond to resonant de Broglie waves. And pontryagin's dualism of functional sets translates schrödinger's uncertainty principle into the principle of certainty=observability.
The basic equation of quantum mechanics is the Schrödinger equation which expresses the wave function Ψ of a quantum system as an eigenfunction of a quantized Hamiltonian operator H : HΨ = λΨ where the (real) eigenvalue λ is the quantum energy of the system in the state Ψ see equations (1.3.2), (1.3.4). Embodied already in this equation is the basic quantum mechanical principle that quantum energies cannot take on arbitrary values but are quantized : they are given by a discrete set of eigenvalues of a suitable second-order differential operator. This mathematical phenomenon of the discreteness of eigenvalues explains, for example, the observed discreteness of absorption and emission atomic spectral lines; compare remarks in Sections 1.2 and 1.3 of Chapter 1. The Schrödinger theory, and the equivalent theory of Heisenberg, Born and Jordan, represents a distinct advancement of the Bohr theory. Some early basic papers on quantum mechanics are compiled in the book [82], which includes a historic introduction by B. van der Waerden. Also see [6, 8, 9, 24, 75, 76]. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
From a combination of Maxwell’s electromagnetism with Planck’s law and the de Broglie hypothesis, we arrive at quantized photonic wave groups whose constant phase velocity is equal to the speed of light c = ω/k and to their group velocity dω/dk. When we include special relativity expressed in simplest units, we find that, for particulate matter, the square of rest mass , i.e., angular frequency squared minus wave vector squared. This equation separates into a conservative part and a uniform responsive part. A wave function is derived in manifold rank 4, and from it are derived uncertainties and internal motion. The function solves four anomalies in quantum physics: the point particle with prescribed uncertainties; spooky action at a distance; time dependence that is consistent with the uncertainties; and resonant reduction of the wave packet by localization during measurement. A comparison between contradictory mathematical and physical theories leads to similar empirical conclusions because probability amplitudes express hidden variables. The comparison supplies orthodox postulates that are compared to physical principles that formalize the difference. The method is verified by dual harmonics found in quantized quasi-Bloch waves, where the quantum is physical; not axiomatic.