Related papers: Two electrons on a hypersphere: a quasi-exactly so…
The quantum mechanics of two Coulomb charges on a plane $(e_1, m_1)$ and $(e_2, m_2)$ subject to a constant magnetic field $B$ perpendicular to the plane is considered. Four integrals of motion are explicitly indicated. It is shown that for…
A flexible multi-parameter exactly solvable model of potential profile, containing an arbitrary number of continuous smoothly shaped barriers and wells, both equal or unequal, characterized by finite values and continuous profiles of the…
We present here novel insight into exchange-correlation functionals in density functional theory, based on the viewpoint of optimal transport. We show that in the case of two electrons and in the semiclassical limit, the exact…
The energy and wave function of a harmonically confined two-electron system coupled to light is calculated by separating the wave functions of the relative and center of mass (CM) motions. The relative motion wave function has a known…
The electron-phonon interaction corresponding to the Holstein model (with Coulomb repulsion) is simulated in infinite dimensions using a novel quantum Monte Carlo algorithm. The thermodynamic phase diagram includes commensurate…
The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules.…
The differential and total cross sections for electron capture by positrons from helium atoms are calculated using a first-order distorted wave theory satisfying the Coulomb boundary conditions. In this formalism a parametric potential is…
We show that a difference in time scales of vertical and lateral dynamics permits one to analyze the problem of interacting electrons confined in an axially symmetric three-dimensional potential with a lateral oscillator confinement by…
We present a general approach for the solution of the three-body problem for a general interaction, and apply it to the case of the Coulomb interaction. This approach is exact, simple and fast. It makes use of integral equations derived…
A new scheme for constructing approximate effective electron potentials within density-functional theory is proposed. The scheme consists of calculating the effective potential for a series of reference systems, and then using these…
The energy dependence of the relaxation rate of hot electrons due to interaction with the Fermi sea is studied. We consider 2D and 3D systems, quasi-1D quantum wires with multiple transverse bands, as well as single-channel 1D wires. Our…
We analyze the effect that the Coulomb interaction has on the edge excitations of an electron gas confined in a bar of thickness $W$, and in presence of a magnetic field corresponding to filling factor 1 Quantum Hall effect. We find that…
The Coulomb energy of a charge that is uniformly distributed on some set is maximized (among sets of given volume) by balls. It is shown here that near-maximizers are close to balls.
Exact solutions are presented of the Dirac equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction n < 1. The found solutions are expressed in terms of new complex…
By an idealized quantum mechanical model, we formally describe the dispersion of nonretarded electromagnetic waves that express charge density oscillations near a fixed plane in three spatial dimensions (3D) at zero temperature. Our goal is…
Results of our recent highly accurate computations of the Coulomb two-center systems with the unit electrical charges $X^{+} X^{+} e^{-}$ and $X^{+} Y^{+} e^{-}$ are discussed. In particular, we have determined (to very high accuracy) the…
We calculate exactly, using finite size techniques, the quantum mechanical and many-body effects to the self-capacitance of a spherical quantum dot in the regime of extreme confinement, where the radius of the sphere is much smaller than…
The form of the wave function at three-electron coalescence points is examined for several spin states using an alternative method to the usual Fock expansion. We find that, in two- and three-dimensional systems, the non-analytical nature…
We propose the notion of $E_{2}$-quasi-exact solvability and apply this idea to find explicit solutions to the eigenvalue problem for a non-Hermitian Hamiltonian system depending on two parameters. The model considered reduces to the…
We obtain exact solution of the Dirac equation with the Coulomb potential as an infinite series of square integrable functions. This solution is for all energies, the discrete as well as the continuous. The spinor basis elements are written…