相关论文: Wave mechanics of the hydrogen atom
Based on an exposition of the underlying physics and applied mathematics in arXiv:1603.00899, this paper in five separate parts presents a description of the properties of the amplitude functions of the hydrogen atom according to wave…
A partial separation of the variables is practicable for the solution of Schroedinger's temporally independent equation in cartesian coordinates x,y,z, which yields moderately simple algebraic formulae for the amplitude functions involving…
The solution of Dirac's equation for the hydrogen atom according to relativistic wave mechanics yields for each state a vectorial amplitude function with four components, two large and two small. Each such component has its characteristic…
In this paper we introduce a new model for the quantum-mechanical system of the hydrogen atom. We start with a four-dimensional Lorentzian quadratic space $(V,q)$ and let $C \subset V$ be the corresponding cone. The Hilbert space of our…
It is shown that all of the basic properties of the hydrogen atom can be consistently described in terms of classical electrodynamics instead of taking the electron to be a particle; we consider an electrically charged classical wave field,…
We study the Hydrogen atom as a quantum mechanical system with a Coulomb like potential, with a semiclassical approach based on an effective description of quantum mechanics. This treatment allows us to describe the quantum state of the…
The purely algebraic technique associated with the creation and annihilation operators to resolve the radial equation of Hydrogen-like atoms (HLA) for generating the bound energy spectrum and the corresponding wave functions is suitable for…
We examine the procedure to construct the variables of use for the momentum representation in quantum mechanics. The momentum variables must be chosen properly conjugate to the corresponding position space variables, such that valid…
The standard solution of the Schroedinger equation for the hydrogen atom is analyzed. Comparing with the recently established internal properties of electrons it is found, that these solutions cannot be seen as physically valid states of…
We construct the integral transform passing from the space representation to the momentum representation for the Hydrogen atom using polar spherical coordinates. The resulting radial wave functions are explicitly given in terms of complex…
Schrodinger's equation predicts something very peculiar about the electron in the Hydrogen atom: its total energy must be equal to zero. Unfortunately, an analysis of a zero-energy wavefunction for the electron in the Hydrogen atom has not…
The Hamiltonian of a pure hydrogen atom possesses the SO(4) symmetry group generated by the integrals of motion: the angular momentum and the Runge-Lenz vector. The pure hydrogen atom is a supersymmetric and superintegrable system, since…
This paper posits the existence of, and finds a candidate for, a variable change that allows quantum mechanics to be interpreted as quantum geometry. The Bohr model of the Hydrogen atom is thought of in terms of an indeterministic electron…
The angular wave functions for a hydrogen atom are well known to be spherical harmonics, and are obtained as the solutions of a partial differential equation. However, the differential operator is given by the Casimir operator of the…
We expose the Schr\"odinger quantum mechanics with traditional applications to Hydrogen atom. We discuss carefully the experimental and theoretical background for the introduction of the Schr\"odinger, Pauli and Dirac equations, as well as…
The O(4) supersymmetry of the hydrogen atom is utilized to construct a complete basis using only the bound state wave functions. For a large class of perturbations, an expansion of the electron (exciton) wave function into such a complete…
In Part one of this Paper a hypothesis is forwarded of the electron charge in an atom existing in a distributed form. To check it by methods of electrodynamics and mechanics (without invoking the formalism of quantum mechanics and the…
By using the multipolar gauge it is shown that the quantum mechanics of an electrically charged particle moving in a prescribed classical electromagnetic field (wave mechanics) may be expressed in a manner that is gauge invariant, except…
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…
In the last few years the hydrodynamic formulation of quantum mechanics, equivalent to the Bohmian equations of motion, has been used to obtain numerical solutions of the Schrodinger equation. Problems, however, have been experienced near…