A Study of Confined Helium Atom

The helium atom confined by a spherical parabolic potential well is studied employing the adiabatic hyperspherical approach method. Total energies of the ground and three low-excited states are obtained as a function of the confined potential radii. We find that the energies of a spherical parabolic potential well are in good agreement with those of an impenetrable spherical box for the larger confined potential radius. We find also that the confinement may cause accidental degeneracies between levels with different low-excited states and the inversion of the energy values. The results for the three-dimensional spherical potential well and the two-dimensional disc-like potential well are compared with each other. We find that the energy difference between states in a two-dimensional parabolic potential is also obviously larger than the corresponding levels for a spherical parabolic potential.     

A Study of Confined Helium Atom

The helium atom confined by a spherical parabolic potential well is studied employing the adiabatic hyperspherical approach method. Total energies of the ground and three low-excited states are obtained as a function of the confined potential radii. We find that the energies of a spherical parabolic potential well are in good agreement with those of an impenetrable spherical box for the larger confined potential radius. We find also that the confinement may cause accidental degeneracies between levels with different low-excited states and the inversion of the energy values. The results for the three-dimensional spherical potential well and the two-dimensional disc-like potential well are compared with each other. We find that the energy difference between states in a two-dimensional parabolic potential is also obviously larger than the corresponding levels for a spherical parabolic potential.     

Calculation of Energies of the Ground and Low Excited States of a Confined Helium Atom in a Spherical Parabolic Well

Making use of the adiabatic hyperspherical approach, we report a calculation for the energy spectrum of the ground and low-excited states of the confined helium atom in a spherical parabolic well. We find that the energies of a spherical parabolic well are in good agreement with those of an impenetrable spherical box for the larger confined potential radius. However, the energy values of a spherical parabolic well are much lower than those of an impenetrable spherical box for small values of re. We also find that the confinement may cause accidental degeneracies between levels with different low-excited states and the inversion of the energy values.     

A Study of a Confined Hydrogen Negative Ion

The ground and three low-excited states of the hydrogen negative ion confined by a spherical harmonic oscillator potential are studied employing the adiabatic hyperspherical approach method. Total energies are obtained as a function of the confined potential radii. We find that the confinement may cause accidental degeneracies between levels with different low-excited states and the inversion of the energy values.     

Feature of a Confined Positronium Negative Ion by a Spherical Parabolic Potential

The ground and three low-excited states of the positronium negative ion confined by a spherical harmonic oscillator potential are studied employing the adiabatic hyperspherical approach method. Total energies are obtained as a function of the confined potential radii. We find that the confinement may cause accidental degeneracies between levels with different Iow-excited states and the inversion of the energy values.     

Effects of an electric field on the confined hydrogen impurity states in a spherical parabolic quantum dot

In this paper, we studied the effects of an electric field on a hydrogenic impurity confined in a spherical parabolic quantum dot using nondegenerate and degenerate perturbation methods. The binding energies of the ground and three low-excited states are calculated as a function of the confinement strength and as a function of the intensity of an applied electric field. Moreover, we computed the oscillator strength and the second-order nonlinear optical rectification coefficient based on the computed energies and wave functions. The results show that the electric and optical properties of hydrogenic impurity states are strongly affected by the confinement strength and the applied electric field.     

Effect of an intense laser field on donor impurities in spherical quantum dots

The effect of an intense laser field on the binding energy of hydrogenic impurity states with an impurity atom located at the center of a spherical quantum dot confined by an infinite barrier potential are studied as a function of the dot radius and of the intensity and frequency of the laser field. Accurate binding energies are obtained for the 1s, 2s and 2p states by numerical integration of the Schrödinger equation. The binding energies are found to increase with decrease in the dot radius, and decrease with increase in the value of the laser field amplitude λ in all cases.     

Energy Spectrum of Helium Confined to a Two-Dimensional Space

Making use of the adiabatic hyperspherical approach, we report a calculation for the energy spectrum of the ground and low-excited states of a two-dimensional helium in a magnetic field. The results show that the ground and low-excited states of helium in low-dimensional space are more stable than those in three-dimensional space and there may exist more bound states.     

Two-dimensional hydrogen negative ion in a magnetic field

Making use of the adiabatic hyperspherical approach, we report a calculation for the energy spectrum of the ground and low-excited states of a two-dimensional hydrogen negative ion H^{-} in a magnetic field. The results show that the ground and low-excited states of H^{-} in low-dimensional space are more stable than those in three-dimensional space and there may exist more bound states.     

Excitons in quantum—dot quantum—well nanoparticles

A variational calculation is presented for the ground-state properties of excitons confined in spherical core-shell quantum-dot quantum-well (QDQW) nanoparticles. The relationship between the exciton states and structure parameters of QDQW nanoparticles is investigated, in which both the heavy-hole and the light-hole exciton states are considered. The results show that the confinement energies of the electron and hole states and the exciton binding energies depend sensitively on the well width and core radius of the QDQW structure. A detailed comparison between the heavy-hole and light-hole exciton states is given. Excellent agreement is found between experimental results and our calculated 1s_e－1s_h transition energies.     

Effect of conduction band parabolicity on the spectrum and binding energy of a hydrogenic impurity in GaAs spherical quantum dots

The energy levels and binding energies of a hydrogenic impurity in GaAs spherical quantum dots with radius R are calculated by the finite difference method. The system is assumed to have an infinite confining potential well with radius R, which can be viewed as a hard wall boundary condition. The parabolicity of the conduction band profile for GaAs material can be viewed as a parabolic potential well. The energy levels and binding energies are depended dramatically on the radius of the quantum dot and the parabolic potential well. The results show that parabolic potential can remarkably alter the energy level ordering and binding energy level ordering of hydrogenic impurity states for the quantum dot with a smaller radius R.     

Electron–hole transition energy for a spherical quantum dot confined in a nano-cylindrical wire

A single-band constant confining potential is applied to InAs spherical quantum dot confined in a GaAs cylindrical nano-wire to determine the electronic structure. The energy eigenvalues and transition energies are numerically calculated as a function of the dot radius. The calculations were performed within the effective mass approximation, using the finite element method. The effect of both spherical and cylindrical confinement, the size dependence of the ground and first excited state energies for electron and heavy hole and transition energies are reported and compared with experimental and theoretical results in relevant conditions.     

界面效应对弱受限球形量子点异质结内电子能级的影响

采用球壳结构和渐变有限深谐振子势阱模型,分析了界面效应对弱受限半导体量子点异质结的束缚态电子基态能级的扰动情况.计算表明,对于处于弱受限的量子点,异质结厚度在30 nm内界面效应明显.当异质结壳层厚度进而增大的时候界面效应的影响将逐渐减弱,受扰动的基态能级间隔逐渐减小,到最后各基态能简并为某一固定值.     

The hydrogen atom confined in both Debye screening potential and impenetrable spherical box

The ground state energy, some low-lying excited state energies and oscillator strengths for a hydrogen atom confined in both a Debye screening potential and finite impenetrable spherical box have been calculated. These have been calculated using a linear variational method based on B-spline basis functions. The results have been compared with those of other authors. The evaluated energies and oscillator strengths with respect to different plasma screening parameters with a certain confinement radii are discussed.     

Spectrum of helium at high pressures

The effect of high pressures on an atom is frequently simulated by enclosing the atom in an impenetrable spherical box. The spectrum of such a confined helium atom placed at the centre of a spherical box is investigated. A model potential is used to calculate the energies of twelve excited states and thereby the transition wavelengths for a range of values of the radius of the confining sphere. Applications of results are discussed. Received 29 August 2002 Published online 10 December 2002 RID="a" ID="a"e-mail: ypvsj@uottawa.ca     

Specific features of determination of the energy of excited electronic states in the formalism of density functional theory

Possibilities for application of the theory of subspaces to determination of the energy of excited electronic states are studied in terms of density functional formalism. Specific features of computer implementation of the theory in a basis of spherical Gaussian functions, whose parameters are determined by minimizing the energy of the corresponding subspace of states, are discussed. The results of calculation of the energy of excited states and the excitation energies of simple atoms and molecules are presented to demonstrate the potential of the approach.     

Exploration of Pseudospin Symmetry in the Resonant States

Taking ^120Sn as an example, we discuss the pseudospin symmetry in the single proton resonant states by examining the energies, widths and the wavefunctions. The information of the single proton resonant states in spherical nuclei are extracted from an analytic continuation in the coupling constant method within the framework of the self-consistent relativistic mean field theory under the relativistic boundary condition. We find small energy splitting in a pair of pseudospin partners in the resonant states. The lower components of the Dirac wavefunctions of a pseudospin doublet agree well in the region where nuclear potential dominates. It is concluded that the pseudospin symmetry is also well conserved for the resonant states in realistic nuclei.     

Fisher information for endohedrally confined hydrogen atom

Electron localization and delocalization of endohedrally confined hydrogen atom has been investigated employing Fisher information theory. Confinement has been modeled using a spherical Gaussian-type potential. B-spline bases expansion method was used to solve the Schrödinger equation to obtain the required energy eigenvalues and the corresponding wave functions. Changes in energies with depths of potential are explained using Hellmann-Feynman theorem. The behavior of Fisher information against the confining potential depths and positions are demonstrated. Moreover, our results show that Fisher information is an effective way to measure the localization of valence electrons.     

Topology and Geometry of Smectic Order on Compact Curved Substrates

Smectic order on arbitrary curved substrate can be described by a differential form of rank one (1-form), whose geometric meaning is the differential of the local phase field of the density modulation. The exterior derivative of 1-form is the local dislocation density. Elastic deformations are described by superposition of exact differential forms. We use the formalism of differential forms to systematically classify and characterize all low energy smectic states on torus as well as on sphere. A two dimensional smectic order confined on either manifold exhibits many topologically distinct low energy states. Different states are not accessible from each other by local fluctuations. The total number of low energy states scales as the square root of the system area. We also address the energetics of 2D smectic on a curved substrate and calculate the mean field phase diagram of smectic on a thin torus. Finally, we discuss the motion of disclinations for spherical smectics as low energy excitations, and illustrate the interesting connection between spherical smectic and the theory of elliptic functions.