Related papers: Bohr's atomic model revisited
We introduce an ad-hoc electrodynamics with advanced and retarded Lienard-Wiechert interactions plus the dissipative Lorentz-Dirac self-interaction force. We study the covariant dynamical system of the electromagnetic two-body problem,…
Hamiltonian of a parametric process describing the interaction of a finite number of optical cavity modes, with the microwave field is proposed. Three-boson interaction is due to electro-optical effect. Analysis of the model is based on the…
The Balmer formula for the spectrum of atomic hydrogen is shown to be analogous to that in Compton effect and is written in terms of the difference between the absorbed and emitted wavelengths. The g-factors come into play when the atom is…
A non-moving electron hydrogen model is proposed, resolving a long standing contradiction (94 years) in the hydrogen atom. This, however, forces to not use the "in an orbit point particle kinetic energy" as the phenomenon responsible for…
In the present work, we studied the q-deformed Morse and harmonic oscillator systems with appropriate canonical commutation algebra. The analytic solutions for eigenfunctions and energy eigenvalues are worked out using time-independent…
The hydrogen molecule contains the basic ingredients to understand the chemical bond, i.e, a pair of electrons. We show a step to understand The Correspondence Principle for chaotic system in the Chemical World. The hydrogen molecule is…
We study the asymptotic behavior of the spectrum of a quantum system which is a perturbation of a spherically symmetric anharmonic oscillator in dimension 2. We prove that a large part of its eigenvalues can be obtained by Bohr-Sommerfeld…
Historically, the eccentricity of Sommerfeld orbits from quantization conditions in either parabolic or spherical coordinates was found to differ in almost all cases. To do the orbit comparison correctly, one must use amended instead of…
Spectral analysis is performed on the Born equation, a strongly singular integral equation modeling the interactions between electromagnetic waves and arbitrarily shaped dielectric scatterers. Compact and Hilbert--Schmidt operator…
The fundamental equations of particle motion lead to a modified Poisson equation including dynamic charge. This charge derives from density oscillations of a particle; it is not discrete, but continuous. Within the dynamic model of hydrogen…
The hydrogen molecules $H_2$ and $(H_2)_2$ are analyzed with electronic correlations taken into account between the $1s$ electrons exactly. The optimal single-particle Slater orbitals are evaluated in the correlated state of $H_2$ by…
An approach to quantization of the damped harmonic oscillator (DHO) is developed on the basis of a modified Bateman Lagrangian (MBL); thereby some quantum mechanical aspects of the DHO are clarified. We treat the energy operator for the…
The Bohr-Sommerfeld rule for a spin system is obtained, including the first quantum corrections. The rule applies to both integer and half-integer spin, and respects Kramers degeneracy for time-reversal invariant systems. It is tested for…
This paper continues the analysis of bound quantum systems started in (T. Yarman, A.L. Kholmetskii and O.V. Missevitch. Going from classical to quantum description of bound charged particles. Part 1: basic concepts and assertions), based on…
Harmonic inversion is introduced as a powerful tool for both the analysis of quantum spectra and semiclassical periodic orbit quantization. The method allows to circumvent the uncertainty principle of the conventional Fourier transform and…
We show, that the canonical invariant part of $\hbar$ corrections to the Gutzwiller trace formula and the Gutzwiller-Voros spectral determinant can be computed by the Bohr-Sommerfeld quantization rules, which usually apply for integrable…
In a recent paper, it has been shown the Schr\"{o}dinger equation for the three-dimensional harmonic oscillator can be simplified through the use of an isometric conformal transformation. Here, it is demonstrated that the same…
In the present article, we describe a method of introducing the harmonic potential into the Klein-Gordon equation, leading to genuine bound states. The eigenfunctions and eigenenergies are worked out explicitly.
We investigate deviations from the plane wave model in the interaction of charged particles with strong electromagnetic fields. A general result is that integrability of the dynamics is lost when going from lightlike to timelike or…
On the basis of the Lorentz equations of motion, the orbit of a charge driven by a generic E.M. field with planar symmetry is formulated and analyzed within the framework of a Lorentzian geometry with a curvature whose order of magnitude is…