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We study how the classical Hamilton's principal and characteristic functions are generated from the solutions of the quantum Hamilton-Jacobi equation. While in the classically forbidden regions these quantum quantities directly tend to the…
An approximation-free, numerically efficient algorithm is presented for the Hamiltonian eigen-states of the Stark-Hydrogen problem describing a quantum particle exposed to the central Coulomb force and a homogeneous external field. As an…
Quantum hydrodynamics is a formulation of quantum mechanics based on the probability density and flux (current) density of a quantum system. It can be used to define trajectories which allow for a particle-based interpretation of quantum…
The dynamics of self-gravitating fluid bodies is described by the Euler-Einstein system of partial differential equations. The break-down of well-posedness on the fluid-vacuum interface remains a challenging open problem, which is…
An approach which allows to include the corrections from non-orthogonality of electron states in contacts and quantum dots is developed. Comparison of the energy levels and charge distributions of electrons in 1D quantum dot (QD) in…
The Jaynes-Cummings model (JCM), one of the paradigms of quantum electrodynamics, was introduced to describe interaction between light and a fictitious two-level atom. Recently it was suggested that the JCM Hamiltonian can be invoked to…
As a realistic model of a quantum system of matter, this paper investigates the gravitational-wave effects on a hydrogen-like atom. By formulating the tetrad formalism of linearized gravity, we naturally incorporate the gravitational-wave…
A harmonic oscillator model in four dimensions is presented for the helium atom to estimate the distance to the inner and outer electron from the nucleus, the angle between electrons and the energy levels. The method is algebraic and is not…
This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum…
The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, $V(q)=\alpha q^n$, where $\alpha$ and $n$ are continuously varying parameters. In the non-relativistic case, the exact…
In this paper, we use Clifford algebra $Cl_{2,0}$ to find the 2D orbit of Hydrogen electron under a Coulomb force and a perturbing circularly polarized electric field of light at angular frequency~$\omega$, which is turned on at time $t =…
A transport methodology to study the electron transport between quantum dots arrays based in Transfer Hamiltonian approach is presented. The interactions between the quantum dots and between the quantum dots and the electrodes are…
In this article, we develop quantum mechanics upon the framework of the quantum mechanical Hamilton-Jacobi theory. We will show, that the Schroedinger point of view and the Hamilton-Jacobi point of view are fully equivalent in their…
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…
We study a quantum mechanical system consisting of up to three identical dipoles confined to move along a helical shaped trap. The long-range interactions between particles confined to move in this one dimension leads to an interesting…
The quantum entanglement entropy of the electrons in one-dimensional hydrogen molecule is quantified locally using an appropriate partitioning of the two-dimensional configuration space. Both the global and the local entanglement entropy…
The interplay between electron correlation and nuclear quantum effects makes our understanding of elemental hydrogen a formidable challenge. Here, we present the phase diagram of hydrogen and deuterium at low temperatures and high-pressure…
An ab initio, three-dimensional quantum mechanical calculation has been performed for the time-evolution of continuum electrons in the fields of moving charges. Here the essential singularity associated with the diverging phase factor in…
Closed-orbit theory provides a general approach to the semiclassical description of photo-absorption spectra of arbitrary atoms in external fields, the simplest of which is the hydrogen atom in an electric field. Yet, despite its apparent…
We study the dispersion of the "temporally stable" coherent states for the hydrogen atom introduced by Klauder. These are states which under temporal evolution by the hydrogen atom Hamiltonian retain their coherence properties. We show that…