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arXiv:1311.0237

Critical Missing Equation of Quantum Physics for Understanding Atomic Structures

Xiaofei Huang

Published Nov 1, 2013• 0 citations
arXivHTMLPDF

Abstract

This paper presents an optimization approach to explain why and how a quantum system evolves from an arbitrary initial state to a stationary state, satisfying the time-independent Schrödinger equation. It also points out the inaccuracy of this equation, which is critial important in quantum mechanics and quantum chemistry, due to a fundamental flaw in it conflicting with the physical reality. The some directions are suggested on how to modify the equation to fix the problem

DOI
10.48550/arxiv.1311.0237

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This paper presents an optimization approach to explain why and how a quantum system evolves from an arbitrary initial state to a stationary state, satisfying the time-independent Schrödinger equation. It also points out the inaccuracy of this equation, which is critial important in quantum mechanics and quantum chemistry, due to a fundamental flaw in it conflicting with the physical reality. The some directions are suggested on how to modify the equation to fix the problem
One of the greatest scientific achievements of physics in the 20th century is the discovery of quantum mechanics. The Schrodinger equation is the most fundamental equation in quantum mechanics describing the time-based evolution of the quantum state of a physical system. It has been found that the time-independent version of the equation can be derived from a general optimization algorithm. Instead of arguing for a new interpretation and possible deeper principle for quantum mechanics, this paper elaborates a few points of the equation as a general global optimization algorithm. Benchmarked against randomly generated hard optimization problems, this paper shows that the algorithm significantly outperformed a classic local optimization algorithm. The former found a solution in one second with a single trial better than the best one found by the latter around one hour after one hundred thousand trials.
This paper presents a global optimization approach to quantum mechanics, which describes the most fundamental dynamics of the universe. It suggests that the wave-like behavior of (sub)atomic particles could be the critical characteristic of a global optimization method deployed by nature so that (sub)atomic systems can find their ground states corresponding to the global minimum of some energy function associated with the system. The classic time-independent Schrodinger equation is shown to be derivable from the global optimization method to support this argument.
The time-independent Schrödinger equation represents a stationary-state equation. The stationary wave functions obtained so far are time independent. Their time-dependence is obtained by means of rather general arguments. Then, stationarystate functions are found. The next step in Newton’s and Euler’s representations of classical mechanics is (to derive) the equation of change of stationary-states. Here, Euler’s principles of stationary-state change are generalized to quantum-mechanical systems. This enables us to derive the quantum-mechanical equation of change of stationary-states. The time-independent Schrödinger equation, i.e, the equation of motion will follow in the next chapter.
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The starting point in a quantum mechanical problem is the construction of a Schrödinger equation. A Schrödinger equation is exactly solvable only for a certain number of simple potentials. In most of the cases the Schrödinger equation can be solved exactly. The solution of the Schrödinger equation for the real systems is usually complicated and often exact solutions. The perturbation theory has been proven to be useful in several fields of theoretical physics and also in chemistry. It provides considerable insight into various phenomena. The main disadvantage of this method is that in certain problems the perturbation series converges slowly or diverges. The splitting of an energy level due to the interaction of the nuclear magnetic dipole and the magnetic field Be produced by the electron orbit current is called the fine structure. The term hyperfine structure is used to describe extremely small splitting of spectral lines.
Illustrations based on the use of radiative waves and oscillating strings are suggested to help explain the physical essence and develop intuitive understanding of the basic principles of quantum mechanics, such as quantization, shape of wavefunctions, and their fundamental features. The proposed approach is based on interference of time-independent or stationary waves, which statistically represent effective quantum mechanical particles. The physical significance of this principle is emphasized by tracing its origin back to the fundamental ideas of E. Schrödinger. The suggested explanations are suitable for chemistry undergraduate students and are compatible with covering optics and Fourier-transform spectroscopy in analytical chemistry classes. Supplemental materials are available for this article. Go to the publisher's online edition of Spectroscopy Letters for the following free supplemental resource: Historical Persperctive.