In this paper, we have completely succeeded in the true understanding of the phenomena of spectra of hydrogen atoms. This problem is the motivation of quantum mechanics 100 years ago. But we know that the quantum mechanics is a curious theory. In order to clear this problem, I create the theory of natural statistical physics. In the present time, we know that we must not use the quantum mechanics. The new age of physics starts just now.
In this paper, we have completely succeeded in the true understanding of the phenomena of spectra of hydrogen atoms. This problem is the motivation of quantum mechanics 100 years ago. But we know that the quantum mechanics is a curious theory. In order to clear this problem, I create the theory of natural statistical physics. In the present time, we know that we must not use the quantum mechanics. The new age of physics starts just now.
In this paper, we study the derivation and the solution of Schrodinger equation of the hydrogen atoms using the theory of Natural Statistical Physics. Using these results, we study the phenomena of the spectra of hydrogen atoms and the phenomena of the stability of hydrogen atoms. Here we consider the system of hydrogen atoms for which we need not to consider the in uence of the outer electro-magnetic eld. This is the case where there is no in uence of outer electro-magnetic eld or where we can neglect the in uence of the outer electro-magnetic eld. In this paper, we succeeded in deriving the Schrodinger equation in the natural and reasonable way by the method of variational calculus. Thereby we can obtain the complete understanding of the phenomena of the spectra of hydrogen atoms and the phenomena of the stability of hydrogen atoms. We remark that the model of the system of hydrogen atoms considered in this paper does not concern with the scattering state of hydrogen atoms. In this paper, Fourier's method plays the fundamental role. For the results of this paper, we refer to Ito[16], [19], [20], [22], [24], [25], [26]. 2010 Mathematics Subject Classi cation. Primary 82D99, 82B99, 81Q99.
In this chapter we review the ideas and discoveries that lead to the development of quantum mechanics. Like other theories in physics, it was motivated by a series of experimental results that were at odds with the prevailing theories of the time. New concepts were introduced to explain those experiments, which in turn led to new experiments and more discoveries. Quantum mechanics took its current shape about 100 years ago and continues to provide a formidable framework for describing not only natural phenomena but also for leading us to new technologies, such as quantum information processing.
Abstract The attempt to explain atomic structure was one of the main motives for the genesis of quantum mechanics (Bohr’s atomic model, spectral lines, etc.); at the same time it represented the first true testing ground for the new theory. The explanation of the existence of discrete atomic levels, their quantitative prediction, understanding of the periodic structure of the elements, the correct interpretation of chemical bonds, etc., can be regarded without exaggeration as one of the greatest achievements of the scientific thought of our time. A door to an entirely new world— that of the atomic and subatomic phenomena—opened, triggering an impressive advance in basic scientific knowledge and modern technology, unprecedented in human history. The very concepts and many of the mathematical tools of quantum mechanics have, in many cases, sprung from the efforts to solve these problems. In this chapter, we study atomic structure, and try to illustrate some of these features.
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.”
Introduction Despite its extraordinary predictive successes, quantum mechanics has, since its inception some seventy years ago, been plagued by conceptual difficulties. The basic problem, plainly put, is this: It is not at all clear what quantum mechanics is about. What, in fact, does quantum mechanics describe? It might seem, since it is widely agreed that the state of any quantum mechanical system is completely specified by its wave function, that quantum mechanics is fundamentally about the behavior of wave functions. Quite naturally, no physicist wanted this to be true more than did Erwin Schrodinger, the father of the wave function. Nonetheless, Schrodinger ultimately found this impossible to believe. His difficulty was not so much with the novelty of the wave function [2, page 156 of [3]]: "That it is an abstract, unintuitive mathematical construct is a scruple that almost always surfaces against new aids to thought and that carries no great message." Rather, it was that
The subject of my talk is the relations between the mathematical theory of extremal problems and the physical theory of quanta.1 The theory of quanta, or quantum mechanics, studies phenomena in the world of bodies of atomic scale. It turned out that the usual notions of motion and the usual methods of description of a mechanical system were inapplicable for such bodies. One needed to find another formulation of the basic laws of nature instead of the old one based on observations of bodies containing a very large number of atoms. The drastic revision of all usual notions of mathematics and physics was required. As a result of this revision and due to the efforts of several scientists such formulation has been found and the theory, which is as elegant and complete as the Newton mechanics is, has been created. This new theory — the new quantum mechanics — contains the Newton mechanics as a limiting case. Although some particular questions and problems remain open, the basic principles and the mathematical technique of the new theory can be considered to be completely established.