A model of the electronic internal structure has been developed, revealing the specific movement mode of electrons outside the nucleus. Building on this, the Bohr's planetary model of the hydrogen atom has been adapted into the Saturn model, suitable for describing multi-center and multi-electron bound systems. It has been discovered that the mathematical formalism of Bohr's old quantum theory and wave mechanics are compatible. A quantum chemistry method has been established to implement this compatibility (where the Saturn model and wave mechanics can complement each other), using this method, the energy eigenvalues of s electrons in atoms and the binding energies and bond lengths of four diatomic molecules such as hydrogen molecules have been successfully calculated. This provides new insights into material structure theory. The aforementioned compatibility could lead to the birth of local realism quantum mechanics.
A model of the electronic internal structure has been developed, revealing the specific movement mode of electrons outside the nucleus. Building on this, the Bohr's planetary model of the hydrogen atom has been adapted into the Saturn model, suitable for describing multi-center and multi-electron bound systems. It has been discovered that the mathematical formalism of Bohr's old quantum theory and wave mechanics are compatible. A quantum chemistry method has been established to implement this compatibility (where the Saturn model and wave mechanics can complement each other), using this method, the energy eigenvalues of s electrons in atoms and the binding energies and bond lengths of four diatomic molecules such as hydrogen molecules have been successfully calculated. This provides new insights into material structure theory. The aforementioned compatibility could lead to the birth of local realism quantum mechanics.
In a previous, primary treatise of the author the mathematical description of electron trajectories in the excited states of the H-atom could be demonstrated, starting from Bohr’s original model but modifying it three dimensionally. In a subsequent treatise, Bohr’s theorem of an unalterable angular momentum h/2π, determining the ground state of the H-atom, was revealed as an inducement by the—unalterable—electron spin. Starting from this presumption, a model of the H2-molecule could be created which exhibits well-defined electron trajectories, and which enabled computing the bond length precisely. In the present treatise, Bohr’s theorem is adapted to the atom models of helium and of neon. But while this was feasible exactly in the case of helium, the neon atom turned out to be too complex for a mathematical modelling. Nevertheless, a rough ball-and-stick model can be presented, assuming electron rings instead of electron clouds, which in the outer shell are orientated as a tetrahedron. It entails the principal statement that the neon atom does not represent a static construction with constant electron distances and velocities, but a pulsating dynamic one with permanently changing internal distances. Thus, the helium atom marks the limit for precisely describing an atom, whereby at and under this limit such a precise description is feasible, being also demonstrated in the author’s previous work. This contradicts the conventional quantum mechanical theory which claims that such a—locally and temporally—precise description of any atom or molecule structure is generally not possible, also not for the H2-molecule, and not even for the H-atom.
The basis for the hydrogen atom planetary model, which represents the development of the Rutherford-Bohr atom model, is presented. The measurements of the atom polarizability, radius, electric and magnetic moments, as well as the Stark and Zeeman effects are given as an argument. The central paragraph of the Article is a comparison of the binding energy obtained based on wave measurement data (the Rydberg constant) and the binding energy obtained by calculation according to the data of the electron charge and mass fundamental constants and applying the principle of momentum conservation. The substantiation of the atom stability is given proceeding from the atom planetary model. The nature and mechanism of the optical spectrum formation is discussed. The substantiation of the fine structure of the hydrogen atom spectral lines is presented, proceeding from the fundamental association between the electric field strength of the electron charge and the speed of its velocity. The origin of the optical spectrum hyperfine structure is discussed within the planetary model. The difficulty in constructing an acceptable theory of the electronic structure of atoms is primarily due to the complexity of obtaining direct information on the atoms internal structure. The point is that the outermost electron shell of an atom behaves itself like an effective screen for external probing electrical fields. This circumstance sharply limits the possibilities of experimental methods for studying the intra-atomic structure. On the other hand, it is imperative that the research methods being employed be non-destructive ones in order to obtain reliable information concerning the structure of atoms. This means that the action on the atom during measurement process must meet the condition of the electron shell perturbation smallness of the atom or ion being investigated. Concerns associated with the inaccessibility of the electronic structure of atoms served as a pretext for a conclusion of the limited possibilities of the empirical method of knowing the internal structure of atoms at the proper time.
In 1926, Schrödinger [365] recognized that the variational theory of elliptical differential equations with fixed boundary conditions could produce a discrete eigenvalue spectrum in agreement with the energy levels of Bohr's model of the hydrogen atom. This conceptually startling amalgam of classical ideas of particle and field turned out to be correct. Within a few years, the new wave mechanics almost completely replaced the ad hoc quantization of classical mechanics that characterized the “old” quantum theory initiated by Bohr. Although the matrix mechanics of Heisenberg was soon shown to be logically equivalent, the variational wave theory became the standard basis of methodology in the physics of electrons. The nonrelativistic Schrödinger theory is readily extended to systems of N interacting electrons. The variational theory of finite N -electron systems (atoms and molecules) is presented here. In this context, several important theorems that follow from the variational formalism are also derived.
In the 1920s, the old quantum theory was gradually being superseded by the new quantum theory. The cornerstone of the old theory was Bohr’s model of the hydrogen atom, which predicted that an electron cannot orbit the proton in the hydrogen atom in any arbitrary fashion. Orbits are “quantized,” meaning that only certain sizes, shapes, and magnetic properties are allowed. The principal quantum number n determined the allowed radii of the orbits, the orbital quantum number l determined the allowed shapes, and the magnetic quantum number m determined the magnetic behavior. Additionally, there is a fourth quantum number s which denotes the fact that the electron has an additional angular momentum, loosely associated with self rotation about its own axis, and that is quantized in units of (1/2)~. The old quantum theory was useful to infer the existence of discrete energy levels in atoms, calculate energy spacings between these levels, and therefore allowed one to interpret atomic spectra. The new quantum theory appeared to be more revolutionary and more powerful. It was triggered by Heisenberg’s discovery of matrix mechanics and Schro¨dinger’s discovery of wave mechanics. These two formalisms would not only predict the quantization of energy and provide a prescription to determine the energy difference between the levels (and thus explain the multiplicity of atomic spectra), but also allow one to calculate easily probabilities of transitions between different quantized energy states. At first, matrix mechanics and wave mechanics looked entirely different in their mathematical appearance and physical meaning. However, Schro¨dinger and Eckart [1] independently showed that the two theories are mathematically equivalent. Toward the end of 1926, Dirac unified the two theories using the concept of state vector and thus established the transformation theory of quantum mechanics. This ultimately had a profound implication for the quantum mechanical (mathematical) recipe to treat spin, as we will show in this chapter. The transformation theory is the mathematical recipe to handle modern quantum mechanics. In Heisenberg’s matrix mechanics, a physical quantity is expressed by a matrix, whereas in Schro¨dinger’s wave mechanics, a physical quantity is expressed by a linear operator. In the unified transformation theory, physical quantities are represented by abstract linear operators called Dirac’s q-numbers, which are linear operators in an infinite-dimensional linear space. Depending upon which types of orthogonal coordinate systems are used in this linear space, either matrix mechanics or wave mechanics emerges.
This paper tries to prove that the existence and properties of the electron’s spin can be established not only as a consequence of relativistic quantum mechanics, but also as a consequence of non-relativistic quantum mechanics of the Hydrogen atom or Hydrogenic atoms. It is, in fact, an extended model of the Hydrogen atom or Hydrogenic atoms. This new model starts from the assumption that to the foundation of atomic structure there is not only a potential of electrical nature, but also a potential of magnetic nature, which, together with the Coulomb potential, determine the movement of electrons around the atomic nucleus. As a consequence of this new model is obtained a non-relativistic theory of Hydrogen atom which takes into account the spin of the electron and leads us to a non-relativistic theory of the atom in agreement with the Stern-Gerlach experiment results. As well the model can be used in order to explain the spectrum of Alkali-atoms.
In this chapter we are going to make a very detailed study of the one-electron atom using relativistic quantum mechanics. The one-electron atom is the simplest bound system that occurs in nature, and plays a central role in both classical and quantum theory. There are two reasons for this. Firstly, it is a model that can be solved exactly at many levels of theory — the classical Bohr atom, the non-relativistic quantum mechanical one-electron atom, and the relativistic one-electron atom with spin zero and spin 1/2. Secondly, most of our understanding of multielectron atoms, molecules and solids is based on this model. Of course, a good description of the hydrogen atom is provided by non-relativistic Schrödinger theory. However, once the relativistic quantum theory had been discovered it was of great importance to validate the theory by describing hydrogen at least as well as Schrödinger theory. As we shall see, the Dirac theory was exceedingly successful in this, and furthermore, at several points in the theory the non-relativistic limit can be taken and the effect of relativity in one-electron atoms can be seen explicitly. This connection with the simpler theory will be made here wherever insight may be gained from doing so. One of the key advances brought about by the advent of quantum theory was that it defined eigenfunctions as well as the eigenvalues predicted by the Bohr theory.