Related papers: Quantum eigenvalues and eigenfunctions of an elect…
Confined geometries such as semiconductor quantum dots are promising candidates for fabricating quantum computing devices. When several quantum dots are in proximity, spatial correlation between electrons in the system becomes significant.…
This paper deals with the relativistic, quantized electromagnetic and Dirac field equations in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. In the consequent…
The theoretical foundations of quantum mechanics and de Broglie--Bohm mechanics are analyzed and it is shown that both theories employ a formal approach to microphysics. By using a realistic approach it can be established that the internal…
We study the three-body Coulomb problem in two dimensions and show how to calculate very accurately its quantum properties. The use of a convenient set of coordinates makes it possible to write the Schr\"{o}dinger equation only using…
The path integral for a point particle in a Coulomb potential is solved in momentum space. The solution permits us to give for the first time a negative answer to an old question of quantum mechanics in curved spaces raised in 1957 by…
In computational molecular science, calculation of electrostatic interactions involving charged atoms - the strongest interactions in condensed phases, is a major bottleneck. We propose a quantum-classical algorithm for fast, yet, accurate…
The generalized pseudospectral method is employed to study spherical confinement in two simple Coulombic systems: (i) well celebrated and heavily studied H atom (ii) relatively less explored Hulth\'en potential. In both instances, arbitrary…
A simple one dimensional model is introduced describing a two particle "atom" approaching a point at which the interaction between the particles is lost. The wave function is obtained analytically and analyzed to display the entangled…
Quantum entanglement is a key resource for quantum technologies, including emerging ground-to-satellite quantum communication. In such a scenario, an important challenge to be overcome is to consider entanglement between two or more quantum…
We propose a simple quantum mechanical equation for $n$ particles in two dimensions, each particle carrying electric charge and magnetic flux. Such particles appear in (2+1)-dimensional Chern-Simons field theories as charged vortex soliton…
Quantum entanglement is a concept commonly used with reference to the existence of certain correlations in quantum systems that have no classical interpretation. It is a useful resource to enhance the mutual information of memory channels…
It is shown that a quantum L\'evy process in a box leads to a problem involving topological constraints in space, and its treatment in the framework of the path integral formalism with the L\'evy measure is suggested. The eigenvalue problem…
Many-particle systems pose commonly known computational challenges in quantum theory. The obstacles arise from the difficulty in finding sets of eigenvalues and eigenvectors of the underlying Hamiltonian while enforcing fermion or boson…
The general formula for the interaction potential between two point electric charges which contains the lowest order corrections to the vacuum polarization is derived and investigated. Analytical derivation of this formula is based on the…
The traditional ambiguity about the bulk electrostatic potentials in crystals is due to the conditional convergence of Coulomb series. The classical Ewald approach turns out to be the first one resolving this task as consistent with a…
With progress towards more compact quantum computing architectures, fundamental questions regarding the entanglement of indistinguishable particles need to be addressed. In a solid state device, this quest is naturally connected to the…
Utilizing an appropriate ansatz to the wave function, we reproduce the exact bound-state solutions of the radial Schrodinger equation to various exactly solvable sextic anharmonic oscillator and confining perturbed Coulomb models in…
We use special quadrature formulas for singular and hypersingular integral to numerically solve the Schr\"{o}dinger equation in momentum space with the linear confinement potential, Coulomb and Cornell potentials. It is shown that the…
A critical study of the wave mechanics of a particle trapped in a 1-D box having infinite potential walls and small flexibility in its size reveals its several important and hither to unknown aspects which could be relevant for better…
A model physical problem is studied in which a system of two electrons is subject either to soft confinement by means of attractive oscillator potentials or by entrapment within an impenetrable spherical box of finite radius $R.$ When hard…