Related papers: Exact solutions for a two-electron quantum dot mod…
It is shown on the basis of the multiplicative renormalization-group method of two-loop order that the low-energy effective Hamiltonian of a strongly coupled local electron-phonon system is mapped to the two-channel Kondo model. A phonon is…
In this paper we prove sharp resolvent estimates for the magnetic Schr\"odinger operator in $\mathbb{R}^d$, $d\ge 3$, with $L^\infty$ short-range electric and magnetic potentials. We also show that these resolvent estimates still hold for…
On the contrary to the common intuition, which suggests that a steep expulsive potential makes quantum states widely delocalized, we demonstrate that one- and two-dimensional (1D and 2D) Schroedinger equations, which include expulsive…
We study an exactly solvable model that can be interpreted as an ideal one-dimensional electron gas confined with an anisotropic quantum wire potential of oscillator-shaped profile. The homogeneous nature of the quantum wire is broken by…
Using the method of the "exact discretization" of the Schr\"odinger equation, we propose a particular discretized version of the N=2 Supersymmetric Quantum Mechanics. After defining the corresponding shape invariance condition, we show that…
The gas of the interacted electrons is usually described within Kohn-Sham approximation by the set of Poisson and Schr\"{o}dinger equations with an effective potential for the single-particle wave functions. The solution of these equations…
We study the energy level structure of two-dimensional charged particles in inhomogeneous magnetic fields. In particular, for magnetic anti-dots the magnetic field is zero inside the dot and constant outside. Such a device can be fabricated…
We study the spin relaxation in an interacting two--dimensional electron gas in a strong magnetic field for the case that the electron density is close to filling just one Landau sub--level of one spin projection, i.e., for filling factor…
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.…
We consider the system of two interacting atoms confined in axially symmetric harmonic trap. Within the pseudopotential approximation, we solve the Schroedinger equation exactly, discussing the limits of quasi-one and quasi-two-dimensional…
Single-layer quantum dot gate potential causes type-II band alignment, i.e. electrostatically confines holes and repels electrons, or vice versa. Hence, the confinement of excitons in gated type II quantum dots involves a delicate balance…
Two super-integrable and super-separable classical systems which can be considered as deformations of the harmonic oscillator and the Smorodinsky-Winternitz in two dimensions are studied and identified with motions in spaces of constant…
According to time-dependent density functional theory, the exact exchange-correlation kernel f$_{xc}$(n, q, $\omega$) determines not only the ground-state energy but also the excited-state energies/lifetimes and time-dependent linear…
We consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schr\"odinger perturbation theory, using the Sturmian…
One-dimensional Schr\"odinger operators with singular perturbed magnetic and electric potentials are considered. We study the strong resolvent convergence of two families of the operators with potentials shrinking to a point. Localized…
Exact-diagonalization calculations for N=3 electrons in anisotropic quantum dots, covering a broad range of confinement anisotropies and strength of inter-electron repulsion, are presented for zero and low magnetic fields. The excitation…
In this paper, we study the Schr\"odinger equation with a new quasi-exactly solvable double-well potential. Exact expressions for the energies, the corresponding wave functions and the allowed values of the potential parameters are obtained…
We discuss double ionization of atoms in strong laser pulses using a reduced dimensionality model. Following the insights obtained from an analysis of the classical mechanics of the process, we confine each electron to move along the lines…
We proposed a distributed approximating functional method for efficiently describing the electronic dynamics in atoms and molecules in the presence of the Coulomb singularities, using the kernel of a grid representation derived by using the…
This work continues to study the set of quasi exactly solvable potentials related to the Eckart, Hult\'{e}n, Rosen-Morse, Coulomb and the harmonic oscillator potentials. We solve the Schr\"{o}dinger equation for each potential and obtain…