Related papers: On the concepts of radial and angular kinetic ener…
We treat the classical dynamics of the hydrogen atom in perpendicular electric and magnetic fields as a celestial mechanics problem. By expressing the Hamiltonian in appropriate action-angle variables, we separate the different time scales…
For systems whose classical dynamics is chaotic, it is generally believed that the local statistical properties of the quantum energy levels are well described by Random Matrix Theory. We present here two counterexamples - the hydrogen atom…
We report a theoretical scheme using a B-spline basis set to improve the poor computational accuracy of circular Rydberg states of hydrogen atoms in the intermediate magnetic field. This scheme can produce high accuracy energy levels and…
For a quantum harmonic oscillator an explicit expression that describes the energy distribution as a coordinate function is obtained. The presence of the energy function poles is shown for the quantum system in domains where the Wigner…
We give a conceptual exposition of aspects of gravitational radiation, especially in relation to energy. Our motive for doing so is that the strong analogies with electromagnetic radiation seem not to be widely enough appreciated. In…
We study the hydrogen atom eigenstate energy and wave function in the Rindler space. The probability distribution is tilted because the electric field of the nucleus is no longer spherically symmetric. The hydrogen atom therefore cannot be…
The dynamics of Rydberg states of a hydrogen atom subject simultaneously to uniform static electric field and two microwave fields with commensurate frequencies is considered in the range of small fields amplitudes. In the certain range of…
The Roentgen term is an often neglected contribution to the interaction between an atom and an electromagnetic field in the electric dipole approximation. In this work we discuss how this interaction term leads to a difference between the…
Gyratonic pp-waves are exact solutions of Einstein's equations that represent non-linear gravitational waves endowed with angular momentum. We consider gyratonic pp-waves that travel in the $z$ direction and whose time dependence on the…
We discuss kinematical properties of a free relativistic particle with deformed phase space in which momentum space is given by (a submanifold of) de Sitter space. We provide a detailed derivation of the action, Hamiltonian structure and…
With regard to generic two-component systems, the theory of first variations of global quantities is reviewed and explicit expressions are inferred for subsystem potential energies and potential-energy tensors. Performing a conceptual…
Classical model of light in helicity formalism is presented. Then quantum point of view at photons -- construction and interpretation of photon wave function is proposed. Quantum mechanics of photon is investigated. The Bia\l ynicki --…
Some typical kinetic energy integrals which arise in the application of extended Hylleraas-configuration interaction (E-Hy-CI) function in the framework of Rayleigh-Ritz method of variation, have been evaluated analytically for two-electron…
A kinetic theory is developed to describe radiating electrons whose motion is governed by the Lorentz-Dirac equation. This gives rise to a generalized Vlasov equation coupled to an equation for the evolution of the physical submanifold of…
The dynamics of a charged relativistic particle in electromagnetic field of a rotating magnetized celestial body with the magnetic axis inclined to the axis of rotation is studied. The covariant Lagrangian function in the rotating reference…
The coherence properties of the classical waves are discussed in terms of the Cauchy problem for the wave equation, and of a discrete representation by an ensemble of Hamiltonian systems. Wave quanta are related to specific "action fields",…
We discuss radiation fields in a compact space of finite size instead of that in a cavity for investigating the coupled atom-radiation field system. Representations of $T(1)\times SO(4)$ group are used to give a formulation for kinematics…
In this work we give a few explicit formulas regarding the radiation fields of linear free waves. We then apply these formulas on the channel of energy theory. We characterize all the radial weakly non-radiative solutions in all dimensions…
Kinetic energy functionals of the electronic density are used to model large systems in the context of density functional theory, without the need to obtain electronic wavefunctions. We discuss the problems associated with the application…
Recently it was shown that the ratio of kinetic and potential energy at the perihelion of a Kepler orbit relates to the ellipse eccentricity. Here, a general expression for the that ratio at any position on the orbit is presented.