Related papers: Obtaining Hydrogen energy wave functions using the…
We present sum rules for Clebsch-Gordan coefficients in the framework of SO(4) group-theoretical description of the hydrogen atom. The main results are obtained using properties of the Runge-Lenz- Pauli vector, in particular expressing the…
It was shown that the Runge-Lenz vector for a hydrogen atom is equivalent to the raising and lowering operators derived from the factorization of radial Schr\"{o}dinger equation. Similar situation exists for an isotropic harmonic…
Using the wave equation as an example, it is shown how to extend the hydrodynamic Lagrangian-picture method of constructing field evolution using a continuum of trajectories to second-order theories. The wave equation is represented through…
The bound state energy eigenvalues for the two-dimensional Kepler problem are found to be degenerate. This "accidental" degeneracy is due to the existence of a two-dimensional analogue of the quantum-mechanical Runge-Lenz vector.…
We generalize Schroedinger's factorization method for Hydrogen from the conventional separation into angular and radial coordinates to a Cartesian-based factorization. Unique to this approach, is the fact that the Hamiltonian is represented…
Consider the problem: why does the bound state spectrum $E(n) < 0$, of hydrogen atom Hamiltonian $H$ have more degenerate eigenstates than those required by rotational symmetry? The answer is well known and was demonstrated by Pauli. It is…
The hydrogen atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the…
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 N=2 supersymmetric extension of the Schr\"odinger-Hamiltonian with 1/r-potential in d dimension is constructed. The system admits a supersymmetrized Laplace-Runge-Lenz vector which extends the rotational SO(d) symmetry to a hidden…
Following Dahl's method an exact Runge-Lenz vector M with two components M and M is obtained as a constant of motion for a two particle-system with charges e and e whose electromagnetic interaction is based on Chern-Simons electrodynamics.…
We derive Huygens' principle for electrodynamics in terms of 4-vector potentials defined as distributions supported on a surface surrounding the charge-current density. By combining the Pauli algebra with distribution theory, a compact and…
General recurrence relations for arbitrary non-diagonal, radial hydrogenic matrix elements are derived in Dirac relativistic quantum mechanics. Our approach is based on a generalization of the second hypervirial method previously employed…
As a serious attempt for constructing a new foundation for describing micro-entities from a causal standpoint, it was explained before in [1, 2, 3] that by unifying the concepts of information, matter and energy, each micro-entity is…
As the simplest atom in nature, the hydrogen atom has been explored thoroughly from the perspective of non-relativistic quantum mechanics to relativistic quantum mechanics. Among the research on hydrogen atom, its energy level is the most…
The standard General Relativity results for precession of particle orbits and for bending of null rays are derived as special cases of perturbation of a quantity that is conserved in Newtonian physics, the Runge-Lenz vector. First this…
We substantiate the need for account of the proper electromagnetic field of the electron in the canonical problem of hydrogen in relativistic quantum mechanics. From mathematical viewpoint, the goal is equivalent to determination of the…
We have derived energy conservation equations from the quaternionic Newton's law that is compatible with Lorentz transformation. This Newton's law yields directly the Euler equation and other equations governing the fluid motion. With this…
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…
Quantum hydrodynamics represents quantum mechanics through two complementary models: the Eulerian picture, a direct transcription of wave mechanics, and the Lagrangian picture, in which the quantum state is represented by the collective…
Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the Dirac form of relativistic quantum mechanics. Our approach is inspired on the relativistic extension of the second hypervirial method that has been…