Related papers: Nonrelativistic quantum particles on the Minkowski…
A novel differential calculus with central inner product is introduced for kappa-Minkowski space. The `bad' behaviour of this differential calculus is discussed with reference to symplectic quantisation and A-infinity algebras. Using this…
I review arguments demonstrating how the concept of "particle" numbers arises in the form of equidistant energy eigenvalues of coupled harmonic oscillators representing free fields. Their quantum numbers (numbers of nodes of the wave…
A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating…
In this short paper I discuss how conformal geometric algebra models for euclidean and minkowski targetspaces determine the allowed quantum mechanical statespaces for free particles. I explicitly treat 2-dimensional euclidean space and…
We have proposed a generally covariant non-relativistic particle model that can represent the $\kappa$-Minkowski noncommutative spacetime. The idea is similar in spirit to the noncommutative particle coordinates in the lowest Landau level.…
We show that in a neutral magnetized plasma there exist microscopic oscillatory modes, with wavelengths of the order of magnitude of the mean interparticle distance, which become unstable when the electron density exceeds a limit…
We consider the quantum problem of a particle in either a spherical box or a finite spherical well confined by a circular cone with an apex angle $2\theta_0$ emanating from the center of the sphere, with $0<\theta_0<\pi$. This non-central…
Two of the most iconic systems of quantum physics are the particle in a box and the Coulomb potential (the third is, of course, the harmonic oscillator). In this expository paper, we consider the quantum solution to the problem of an…
The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat…
We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions. We review the…
The eigenstates of a real or complex cubic anharmonic oscillator are investigated using original and alternative methods. The procedure consists of determining global solutions of the Schr\"odinger equation that comply with the pertinent…
We study a relativistic quantum particle in cosmic string spacetime in the presence of a uniform magnetic field and a Coulomb-type scalar potential. It is shown that the radial part of this problem possesses the $su(1,1)$ symmetry. We…
We present an exact treatment of the influences on a quantum scalar field in its Minkowski vacuum state induced by coupling of the field to a uniformly accelerated harmonic oscillator. We show that there are no radiation from the oscillator…
A consistent theory, which describes the incoherent scattering of classically moving relativistic particles by the nuclei of crystal planes without any phenomenological parameter is presented. The basic notions of quantum mechanics are…
Eigenfunctions and eigenvalues of the free magnetic Schr\"odinger operator, describing a spinless particle confined to an infinite layer of fixed width, are discussed in detail. The eigenfunctions are realized as an orthonormal basis of a…
This paper examines the properties of the self-energy operator in lattice-matched semiconductor heterostructures, focusing on nonanalytic behavior at small values of the crystal momentum, which gives rise to long-range Coulomb potentials. A…
We investigate the relativistic effects of a moving particle in the field of a pseudo-harmonic oscillatory ring-shaped potential under the spin and pseudo-spin symmetric Dirac wave equation. We obtain the bound state energy eigenvalue…
Low energy spectra of isotropic quantum dots are calculated in the regime of low electron densities where Coulomb interaction causes strong correlations. The earlier developed pocket state method is generalized to allow for continuous…
Assuming the charged particle to be a two-dimensional oscillator that scatters the classical background of zero-point field one can deduce the Coulomb force of the two interacting particles. The correct deduction of the force is conditioned…
Motivated by a recent analysis which presents explicitly the general solution, we consider the eigenvalue problem of the spinless Salpeter equation with a ("hard-core amended") Coulomb potential in one dimension. We prove the existence of a…