Related papers: On the N-dimensional hydrogen atom in momentum rep…
A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigenvalue equation. Each of these components are found to satisfy a generalized wave equation of the form…
A method for computing the Hankel transform is proposed whereby the letter is reduced to a sum by representing the integrand as a smooth function times a Bessel function. The smooth function is replaced by its wavelet decomposition with a…
The hydrogen atom is investigated, within a pseudo-complex extension of the coordinates and momenta, which introduces a minimal length scale (l) and results into a non-commutative Quantum Mechanics. After resuming the pseudo-complex…
An exact expression for the phase of an atomic interferometer located in a non-inertial reference frame (platform) moving along an arbitrary trajectory and with an orientation that changes arbitrarily over time is obtained. This expression…
We extend a method (E. Canc\`es and L.R. Scott, SIAM J. Math. Anal., 50, 2018, 381--410) to compute more terms in the asymptotic expansion of the van der Waals attraction between two hydrogen atoms. These terms are obtained by solving a set…
We transform the Schr\"odinger wave equation to a nine-parameter Heun-type differential equation. Using our solutions of the latter in [J. Math. Phys. 59 (2018) 113507], we are able to identify the associated potential function, energy…
In this paper, we investigate the transformation laws of the Wigner function under changes of reference frames. By employing the coordinate transformation of the wave functions, we derive an integral representation for the transformed…
Using a new result on the integral involving the product of Bessel functions and associated Laguerre polynomials, published in the mathematical literature some time ago, we present an alternative method for calculating discrete-discrete…
By introducing the thermo entangled state representation, we derived four new photocount distribution formulas for a given density operator of light field. It is shown that these new formulas, which is convenient to calculate the…
Ionization of atoms and molecules by absorption of a light pulse results in electron wavepackets carrying information on the atomic or molecular structure as well as on the dynamics of the ionization process. These wavepackets can be…
A phase-space representation of nuclear interactions, which depends on the distance $\vec{r}$ and relative momentum $\vec{p}$ of the nucleons, is presented. A method is developed that permits to extract the interaction $V(\vec{r},\vec{p})$…
We consider the 1D Tonks-Girardeau gas with a space-dependent potential out of equilibrium. We derive the exact dynamics of the system when divided into $n$ boxes and decomposed into energy eigenstates within each box. It is a…
In this paper, the geometric phase of thermal state in hydrogen atom under the effects of external magnetic field is considered. Especially the effects of the temperature upon the geometric phase is discussed. Also we discuss the time…
Considering that gravitational force might deviate from Newton's inverse-square law and become much stronger in small scale, we present a method to detect the possible existence of extra dimensions in the ADD model. By making use of an…
Taking into account results of WKB-approximation, we derive exact quantum energies and wave functions of even and odd states in the one-dimensional Coulomb potential
Attosecond chronoscopy typically utilises interfering two-photon transitions to access the phase information. Simulating these two-photon transitions is challenging due to the continuum-continuum transition term. The hydrogenic…
It is proved that when solving Schroedinger equations for radially symmetric potentials the effect of higher dimensions on the radial wave function is equivalent to the effect of higher angular momenta in lower dimensional cases. This…
In a recent paper, A. Akbari, N. H. March and A. Rubio [Phys. Rev. A. 76, 032510 (2007)] have investigated the one-electron reduced density-matrix and the momentum density of several two-electron model atoms, including the Hooke's atom. The…
The N-jettiness event shape divides phase space into N+2 regions, each containing one jet or beam. Using a geometric measure these regions correspond to jets with circular boundaries. We give a factorization theorem for the cross section…
We use the density functional method to examine the properties of the nonuniform (two-phase) fluid of two-level atoms, a part of which is excited. Basing on the analysis of the equation of state of a gas of two-level atoms, a part of which…