Some first principles that, we believe, could serve as foundation for quantum theory of extended particles are formulated. It is also shown that in the point-like particles limit the non-relativistic quantum mechanics can be restored. As an illustration the soliton model of hydrogen atom is considered.
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.
Abstract The simple hydrogen atom has had a great influence on the development of quantum theory, particularly in the first half of the twentieth century when the foundations of quantum mechanics were laid. As measurement Fine structure Further reading Exercises techniques improved, finer and finer details were resolved in the spectrum of hydrogen until eventually splittings of the lines were observed that cannot be explained even by the fully relativistic formulation of quantum mechanics, but require the more advanced theory of quantum electrodynamics. In the first chapter we looked at the BohrSommerfeld theory of hydrogen that treated the electron orbits classically and imposed quantisation rules upon them.
The hydrogen atom with the Coulomb interaction is one of the exactly solvable non-relativistic quantum models. Unlike many other exactly solvable models it describes a real physical object providing the formulas for energy levels and stationary state wave functions of a real hydrogen atom. In this paper we modify the model replacing the Coulomb interaction by the interaction of the proton and the electron with the classical electromagnetic field serving as an intermediary transmitting the electromagnetic interaction of these two charged quantum particles.
Recently a new formulation of quantum mechanics has been suggested which is based on the concept of signed particles, that is, classical objects provided with a position, a momentum and a sign simultaneously. In this article, we comment on the plausibility of simulating atomic systems beyond the Born–Oppenheimer approximation by means of the signed particle formulation of quantum mechanics. First, to show the new perspective offered by this new formalism, we provide an example studying quantum tunnelling through a simple Gaussian barrier in terms of the signed particle formulation. Then, we perform a direct simulation of the hydrogen atom as a full quantum two-body system, showing that the formalism can be a very promising tool for first-principle-only quantum chemistry.
The purpose of this work is to retrace the steps that were made by scientists of XX century, like Bohr, Schrodinger, Heisenberg, Pauli, Dirac, for the formulation of what today represents the modern quantum mechanics and that, within two decades, put in question the classical physics. In this context, the study of the electronic structure of hydrogen atom has been the main starting point for the formulation of the theory and, till now, remains the only real case for which the quantum equation of motion can be solved exactly. The results obtained by each theory will be discussed critically, highlighting limits and potentials that allowed the further development of the quantum theory.
The initial purpose is to add two physical origins for the outstandingly clear mathematical description that Dirac has left in his Principles of Quantum Mechanics. The first is the “internal motion” in the wave function of the electron that is now expressed through dispersion dynamics; the second is the physical origin for mathematical quantization. Bohr’s model for the hydrogen atom was “the greatest single step in the development of the theory of atomic structure.” It leads to the Schrodinger equation which is non-relativistic, but which conveniently equates together momentum and electrostatic potential in a representation containing mixed powers. Firstly, we show how the equation is expansible to approximate relativistic form by applying solutions for the dilation of time in special relativity, and for the contraction of space. The adaptation is to invariant “harmonic events” that are digitally quantized. Secondly, the internal motion of the electron is described by a stable wave packet that implies wave-particle duality. The duality includes uncertainty that is precisely described with some variance from Heisenberg’s axiomatic limit. Harmonic orbital wave functions are self-constructive. This is the physical origin of quantization.