Related papers: On the N-dimensional hydrogen atom in momentum rep…
Diffusion rates are calculated on the basis of van Hove's formula for the dynamical structure factor (DSF) related to particle scattering at mobile adsorbates. The formula is evaluated quantum mechanically using eigenfunctions obtained from…
We scrutinize the behaviour of hydrogen atom's eigenvalues in a quantum plasma as it interacts with electric field directed along $\theta=\pi$ and exposed to linearly polarized intense laser field radiation. Using the Kramers-Henneberger…
High accuracy helium wave functions based on exponentials with random coefficients are transformed into momentum space. The utility of the wave functions is demonstrated through calculation of the expectation value of various operators…
Consider a homogenous fluid membrane, or vesicle, described by the Helfrich-Canham energy, quadratic in the mean curvature. When the membrane is axially symmetric, this energy can be viewed as an `action' describing the motion of a…
We extend the usual Kustaanheimo-Stiefel $4D\to 3D$ mapping to study and discuss a constrained super-Wigner oscillator in four dimensions. We show that the physical hydrogen atom is the system that emerges in the bosonic sector of the…
The electromagnetic N-$\Delta$ transition form factors are calculated in the framework of a formally covariant constituent diquark model. As a spin-3/2 particle the $\Delta$ is assumed to be a bound state of a quark and an axial-vector…
The light-cone wave function of the nucleon is calculated in the limit N_c -> infinity in the quark-soliton model inspired by the theory of the instanton vacuum of QCD. The technique of the finite time evolution operator is used in order to…
Using heuristic arguments alone, based on the properties of the wavefunctions, we obtain the energy eigenvalues and the corresponding eigenfunctions of the one-dimensional harmonic oscillator. This approach is considerably simpler and is…
Wave particle duality remains a central interpretational challenge in quantum theory. In this work, we develop a trajectory-based description of photon dynamics formulated in an extended complex space within the relativistic quantum…
The density of states and other thermodynamic functions of helium nanodroplets are calculated for a microcanonical ensemble with both energy and total angular momentum treated as conserved quantum numbers. These functions allow angular…
The dynamic hyperpolarizability of a particle bound by the one-dimensional $\delta$-function potential is obtained in closed form. On the first step, we analyze the singular structure of the non-linear response function as given by the…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
In the Wigner framework, one abandons the assumption that the usual canonical commutation relations are necessarily valid. Instead, the compatibility of Hamilton's equations and the Heisenberg equations are the starting point, and no…
Integral transforms arising from the separable solutions to the Helmholtz differential equation are presented. Pairs of these integral transforms are related via Plancherel theorem and, ultimately, any of these integral transforms may be…
We consider a quantum system coupled to a dissipative background with many degrees of freedom using the Monte Carlo Wave Function method. Instead of dealing with a density matrix which can be very high-dimensional, the method consists of…
The magnetic field generated by an electron bound in a spherically symmetric potential is calculated for eigenstates of the orbital and total angular momentum. General expressions are presented for the current density in such states and the…
We introduce atoms for dyadic atomic $H^1$ for which the equivalence between atomic and maximal function defnitions is dimension independent. We give the sharp, up to $\log(d)$ factor, estimates for the $H^1 \to L^1$ norm estimates for the…
In this article we are going to study the FEM solution to the Density Functional description of Helium. Solving self-consistently including electron-electron repulsion and exchange-correlation effects. This project will be split in four…
In the present manuscript, we employ the Feynman path integral method to derive the propagator in one-dimensional Wigner-Dunkl quantum mechanics. To verify our findings we calculate the propagator associated with the free particle and the…
The Wigner eigenfunctions of a free quantum particle propagating on a plane are derived. Two possibilities are analysed. Firstly, the particle of given energy and angular momentum is discussed. In that case, a special choice of coordinates…