Related papers: Hydrogen in a cavity
Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…
The dynamical equations describing the evolution of a self-gravitating fluid can be rewritten in the form of a Schrodinger equation coupled to a Poisson equation determining the gravitational potential. This wave-mechanical representation…
We illustrate the description of correlated subsystems by studying the simple two-body Hydrogen atom. We study the entanglement of the electron and proton coordinates in the exact analytical solution. This entanglement, which we quantify in…
The Euler-Heisenberg black holes with quantum electrodynamics (QED) correction are embraced by a cavity in this paper, which serves as a boundary of the black hole spacetime and contributes to the equilibrium of the system. We explore the…
The black hole model with a self-gravitating charged spherical symmetric dust thin shell as a source is considered. The Schroedinger-type equation for such a model is derived. This equation appeared to be a finite differences equation. A…
This paper proposes a method for studying the early stages of the cavitation development in arbitrary, non-stationary conditions. This method is based on the comparison of the results of calculations in the framework of a theoretical model…
The dynamics of a particle in an expanding cavity is investigated in the Klein-Gordon framework in a regime in which the single particle picture remains valid. The cavity expansion represents a time-dependent boundary condition for the…
A qualitative model is proposed for a pair of atoms: oxygen and hydrogen in a single-mode optical cavity, bound by one valence electron and immersed in a thermal bath. The interaction of an electron with the cavity field depends on the…
It is shown fields that cannot be represented over one complex plane can be further decomposed for representation over multiple complex planes. This finding is demonstrated here by solving of the Schr\"{o}dinger equation for the hydrogen…
Accurate and predictive computations of the quantum-mechanical behavior of many interacting electrons in realistic atomic environments are critical for the theoretical design of materials with desired properties, and require solving the…
A trajectory in the Schroedinger wave for an electron in an attractive Coulomb potential with the dynamical behavior is proposed and illustrated for a scattering and a bound state. The scattering cross section derived from the trajectories…
We present numerical results for the equation of state of an infinite chain of hydrogen atoms. A variety of modern many-body methods are employed, with exhaustive cross-checks and validation. Approaches for reaching the continuous space…
When a thermodynamic system is released from any constraint, after some time its evolution will render it into an equilibrium state. Although the description of this relaxation to thermodynamic equilibrium has been attempted through both…
Wave mechanics of a particle in an impenetrable spherical cavity with and without a hard core scattering potential of size $\epsilon$ ($\epsilon$ $\to$ 0) at its center is critically analyzed. It makes marginal but important modifications…
Hydrogen atom is studied as a quantum-classical hybrid system, where the proton is treated as a classical object while the electron is regarded as a quantum object. We use a well known mean-field approach to describe this hybrid hydrogen…
The Schroedinger equation is solved exactly within the Born-Oppenheimer approximation for a simulacrum of the $H_3^{++}$-ion. The ion is assumed to form an isosceles triangle and the ground state energy is obtained over its geometrical…
We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two…
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the…
We re-examine the justification for the imposition of regular boundary conditions on the wavefunction at the Coulomb singularity in the treatment of the hydrogen atom in non-relativistic quantum mechanics. We show that the issue of the…
Cavity quantum electrodynamics of multipartite systems is studied in depth, which consist of an arbitrary number of emitters in interaction with an arbitrary number of cavity modes. The governing model is obtained by taking the full…