Related papers: A geometric algebra approach to the hydrogen atom
Choosing the appropriate geometry in which to express the equations of fundamental physics can have a determinant effect on the simplicity of those equations and on the way they are perceived. The point of departure in this paper is the…
This is a paper about geometry and how one can derive several fundamental laws of physics from a simple postulate of geometrical nature. The method uses monogenic functions analysed in the algebra of 5-dimensional spacetime, exploring the…
The presentation makes use of geometric algebra, also known as Clifford algebra, in 5-dimensional spacetime. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from…
Monogenic functions are functions of null vector derivative and are here analysed in the geometric algebra of 5-dimensional spacetime, G(4,1), in order to derive several laws of fundamental physics. The paper introduces the working algebra…
The paper uses geometrical arguments to derive equations with relevance for cosmology; 5-dimensional spacetime is assumed because it has been shown in other works to provide a setting for significant unification of different areas of…
This paper surveys the application of geometric algebra to the physics of electrons. It first appeared in 1996 and is reproduced here with only minor modifications. Subjects covered include non-relativistic and relativistic spinors, the…
A new simplified approach for teaching electromagnetism is presented using the formalism of geometric algebra (GA) which does not require vector calculus or tensor index notation, thus producing a much more accessible presentation for…
In a recent publication the I showed how the geometric algebra ${G}_{4,1}$, the algebra of 5-dimensional space-time, can generate relativistic dynamics from the simple principle that only null geodesics should be allowed. The same paper…
We consider a hydrogen atom in the background spacetimes generated by an infinitely thin cosmic string and by a point-like global monopole. In both cases, we find the solutions of the corresponding Dirac equations and we determine the…
We present exact energy spectrum and eigenfunctions of the one-dimensional hydrogen atom in the presence of the minimal length uncertainty. By requiring the self-adjointness property of the Hamiltonian, we completely determine the…
The hydrogen atom is supposed to be described by a generalization of Schr\"{o}dinger equation, in which the Hamiltonian depends on an iterated Laplacian and a Coulomb-like potential $r^{-\beta}$. Starting from previously obtained solutions…
There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…
The hypothesis is suggested that the equation for the Dirac free wave field is, in fact, a group-theoretical relation describing propagation of specific microscopic deviations of space geometry from the euclidean one (closed topological…
Thanks to the Dirac equation, the hydrogen-like atom at high $Z$ offers a precise model of relativistic bound state, allowing to test properties of unpolarized and polarized structure functions analogous to the hadronic ones, in particular:…
The bound eigenfunctions and spectrum of a Dirac hydrogen atom are found taking advantage of the $SU(1, 1)$ Lie algebra in which the radial part of the problem can be expressed. For defining the algebra we need to add to the description an…
In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.
It is the author's belief that a perfect theory will eventually be formulated, where geometry and physics become indistinguishable, so that the complete understanding of space properties, together with proper assignments between geometric…
We touch upon a long-standing question of the "true" one-dimensional hydrogen atom solution. From a symmetry point of view, Kepler problem in $d\ge2$ dimension is characterized by geometrical rotational symmetry, $SO(d)$, as well as…
A method to construct a geometric structure with the same solutions as a given variational principle is presented. The method applies to large families of variational principles. In particular, the known results that assign cosymplectic…
This article reports on a student summer project performed in 2006 at the University of Frankfurt. It is addressed to undergraduate students familiar with the basic principles of relativistic quantum mechanics and general relativity. The…