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Journal of Henan Normal University

Complex Function Based on the Analysis of Quantum

Cheng-Sheng Liang

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

This article in accordance with the principle law of elements,in complex variable function construction of periodic structure's power function and logarithmic function,has given Principle Quantum Number n,Angular Quantum Number l,Magnetic Quantum Number m and Spin Quantum Number ms,as well as the relationships between them.Amendments to the old quantum theory of the quantum rules,make conclusions and experimental results and quantum mechanics consistent.Without the introduction of magnetic charges,the magnetic flux quantum rules are given,The establishment of magnetic flux quantum and the Principle Quantum Number n,Angular Quantum Number l,Magnetic Quantum Number m and Spin Quantum Number ms relationship are the result.

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This article in accordance with the principle law of elements,in complex variable function construction of periodic structure's power function and logarithmic function,has given Principle Quantum Number n,Angular Quantum Number l,Magnetic Quantum Number m and Spin Quantum Number ms,as well as the relationships between them.Amendments to the old quantum theory of the quantum rules,make conclusions and experimental results and quantum mechanics consistent.Without the introduction of magnetic charges,the magnetic flux quantum rules are given,The establishment of magnetic flux quantum and the Principle Quantum Number n,Angular Quantum Number l,Magnetic Quantum Number m and Spin Quantum Number ms relationship are the result.
Complex numbers are an intrinsic part of the mathematical formalism of quantum theory and are perhaps its most characteristic feature. In this article, we show that the complex nature of the quantum formalism can be derived directly from the assumption that a pair of real numbers is associated with each sequence of measurement outcomes, with the probability of this sequence being a real-valued function of this number pair. By making use of elementary symmetry conditions, and without assuming that these real number pairs have any other algebraic structure, we show that these pairs must be manipulated according to the rules of complex arithmetic. We demonstrate that these complex numbers combine according to Feynman's sum and product rules, with the modulus-squared yielding the probability of a sequence of outcomes.
Abstract The new quantum mechanics consists of a scheme of equations which are very closely analogous to the equations of classical mechanics, with the funda­mental difference that the dynamical variables do not obey the commutative law of multiplication, but satisfy instead the well-known quantum conditions. It follows that one cannot suppose the dynamical variables to be ordinary numbers (c-numbers), but may call them numbers of a special type (q-numbers). The theory shows that these q-numbers can in general be represented by matrices whose elements are c-numbers (functions of a time parameter). When one has performed the calculations with the q-numbers and obtained all the matrices one wants, the question arises how one is to get physical results from the theory, i. e., how can one obtain c-numbers from the theory that one can compare with experimental values ? Hitherto this has been done with the help of a number of special assumptions. In Heisenberg’s original matrix mechanics it was assumed that the elements of the diagonal matrix that repre­sents the energy are the energy levels of the system, and the elements of the matrix that represents the total polarisation, which are periodic functions of the time, determine the frequencies and intensities of the spectral lines in analogy to the classical theory. Schrodinger’s wave representation of the quantum mechanics has provided new ways of obtaining physical results from the theory, based on the assumption that the square of the amplitude of the wave function can in certain cases be interpreted as a probability. From this assumption one can, for instance, work out the probability of a transition being produced in a system (or the number of transitions produced in an assembly of like systems) by an arbitrary external perturbing force, and can thus, by supposing the perturbation to consist of incident radiation, obtain directly Einstein’s B coefficients. Again in Born’s treatment of collision problems it is assumed that the square of the amplitude of the wave function scattered in any direction determines the probability of the colliding electron (or other body) being scattered in that direction.
The foundations of quantum mechanics are analyzed, and some problems that appeared during its crea-tion and remain unsolved today are emphasized. It is shown that the introduction of variable wave number k, depending on electron coordinates, and the omission of the azimuth part of the wave function ̂ ψ, were erro-neous. Including the azimuth factor of the wave function and taking into consideration the constant value of k result in wave-equation solutions showing a discrete nodal structure of intratomic space, and arrives at a peri-odic-nonperiodic law for behavior of atomic structures. Viewing atoms as quasi-spherical neutron molecules makes it possible to understand characteristic features of the periodic table. PACS Numbers: 03.65.Bz, 03.65.Ge 1.
Abstract The development of the complex of assumptions and methods now referred to as the “old quantum theory” mainly took place in the first five years following the introduction of the Bohr atomic model in 1913. Three guiding principles emerged that were used, sometimes in overlapping ways, to explain the flood of spectroscopic data that needed to be explained. First, quantization rules (or conditions) were proposed to single out the allowed orbital motions of electrons in atoms. These rules were derived in various forms by Planck, Sommerfeld, and Wilson, but were put into their most general form by Schwarzschild, who recognized the underlying principle as the quantization of the action variables of a multiply periodic classical system. Second, the special role of the action variables in quantization was given convincing support by the transfer of the adiabatic principle of mechanics to quantum theory (work primarily due to Paul Ehrenfest). Third, the correspondence principle, or statement of asymptotic coincidence of quantum and classical theory in the limit of large quantum numbers, originally introduced by Bohr in 1913 as a supporting argument for his quantization of angular momentum in his theory of the hydrogen atom, was extended by Bohr and Kramers to provide selection rules and approximate intensity predictions evening the regime low quantum numbers.
This paper aims to provide a thorough critical analysis of two foundational concepts in modern physics — the Landé g-factor and the electron spin quantum number 1/2. Through meticulous historical examination and logical analysis, this paper argues that these concepts are essentially mathematical fitting parameters introduced to bridge the gap between the old quantum theory and experimental data, lacking a solid foundation in physical mechanism. The core contradiction lies in the subsequent development of wave mechanics, which concluded that "the orbital angular momentum of the hydrogen atom ground state is zero," a conclusion that fundamentally conflicts with observational facts such as the Stern-Gerlach experiment, forcing the spin concept to assume a "remedial" role it never needed to bear. As a solution, this paper presents a new framework based on the "Great Tao Model" and the "Unified Theory of Atomic and Molecular Structure." This framework firmly returns to the realism of classical physics, affirms the orbital motion of electrons around the nucleus and their intrinsic angular momentum, and interprets spin as a real mechanical motion. Crucially, this theory naturally derives the universal magnetic moment-angular momentum relation μ = (e/m) L from the "Existence Field" principle, eliminating the need for any artificial correction factors. Based on this, the paper successfully provides a unified and self-consistent explanation for key phenomena such as the Stern-Gerlach experiment and the normal and anomalous Zeeman effects, thereby achieving a simpler and more fundamental description of physics at the atomic scale.