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.     

Intense laser effects on donor impurity in a cylindrical single and vertically coupled quantum dots under combined effects of hydrostatic pressure and applied electric field

Using the effective mass and parabolic band approximations and a variational procedure we have calculated the combined effects of intense laser radiation, hydrostatic pressure, and applied electric field on shallow-donor impurity confined in cylindrical-shaped single and double GaAs-Ga_1−xAl_xAs QD. Several impurity positions and inputs of the heterostructure dimensions, hydrostatic pressure, and applied electric field have been considered. The laser effects have been introduced by a perturbative scheme in which the Coulomb and the barrier potentials are modified to obtain dressed potentials. Our findings suggest that (1) for on-center impurities in single QD the binding energy is a decreasing function of the dressing parameter and for small dot dimensions of the structures (lengths and radius) the binding energy is more sensitive to the dressing parameter, (2) the binding energy is an increasing/decreasing function of the hydrostatic pressure/applied electric field, (3) the effects of the intense laser field and applied electric field on the binding energy are dominant over the hydrostatic pressure effects, (4) in vertically coupled QD the binding energy for donor impurity located in the barrier region is smaller than for impurities in the well regions and can be strongly modified by the laser radiation, and finally (5) in asymmetrical double QD heterostructures the binding energy as a function of the impurity positions follows a similar behavior to the observed for the amplitude of probability of the noncorrelated electron wave function.     

Intense laser field effect on impurity states in a semiconductor quantum well: transition from the single to double quantum well potential

In this work are studied the intense laser effects on the impurity states in GaAs-Ga_{1− x} Al _x As quantum wells under applied electric and magnetic fields. The electric field is taken oriented along the growth direction of the quantum well whereas the magnetic field is considered to be in-plane. The calculations are made within the effective mass and parabolic band approximations. The intense laser effects have been included through the Floquet method by modifying the confinement potential associated to the heterostructure. The results are presented for several configurations of the dimensions of the quantum well, the position of the impurity atom, the applied electric and magnetic fields, and the incident intense laser radiation. The results suggest that for fixed geometry setups in the system, the binding energy is a decreasing function of the electric field intensity while a dual monotonic behavior is detected when it varies with the magnitude of an applied magnetic field, according to the intensity of the laser field radiation.     

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.     

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.     

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.     

Hydrostatic pressure and electric and magnetic field effects on the binding energy of a hydrogenic donor impurity in InAs Pöschl-Teller quantum ring

We consider the effects of electric and magnetic fields as well as of hydrostatic pressure on the donor binding energy in InAs Pöschl-Teller quantum rings. The ground state energy and the electron wave function are calculated within the effective mass and parabolic band approximations, using the variational method. The binding energy dependencies on the electric field strength and the hydrostatic pressure are reported for different values of quantum ring size and shape, the parameters of the Pöschl-Teller confining potential, and the magnetic field induction. The results show that the binding energy is an increasing or decreasing function of the electric field, depending on the chosen parameters of the confining potential. Also, we have observed that the binding energy is an increasing/decreasing function of hydrostatic pressure/magnetic field induction. Likewise, the impurity binding energy behaves as an increasing/decreasing function of the inner/outer radii of the quantum ring nanostructure.     

施加电场的半抛物量子阱中的电光效应

利用量子力学中的紧致密度矩阵方法，研究了施加电场的半抛物量子阱中的电光效应。通过位移谐振子变换，得到了系统中的电子态的精确解。对典型的GaAs材料进行数值计算的结果表明，随着电场强度的增加，电光效应系数几乎线性随之增加；但是随着半抛物量子阱受限势频率的增加，电光效应系数单调地减小；而且在同样的电场强度及抛物束缚势频率作用下，半抛物量子阱模型中的电光效应系数比抛物量子阱模型中的值大两个数量级，这是由于我们所选模型本身的非对称性以及电场进一步使这种非对称性增强的缘故。     

Effects of Electric Field on Electronic States in a GaAs/GaAlAs Quantum Dot with Different Confinements

Binding energies of shallow hydrogenic impurity in a GaAs/GaAlAs quantum dot with spherical confinement, parabolic confinement and rectangular confinement are calculated as a function of dot radius in the influence of electric field. The binding energy is calculated following a variational procedure within the effective mass approximation along with the spatial depended dielectric function. A finite confining potential well with depth is determined by the discontinuity of the band gap in the quantum dot and the cladding. It is found that the contribution of spatially dependent screening effects are small for a donor impurity and it is concluded that the rectangulax confinement is better than the parabolic and spherical confinements. These results are compared with the existing literature.     

A Negative Donor Center Trapped by a Spherical Quantum Dot

The properties of the low-lying states of a negative donor center trapped by a spherical quantum dot, which is subjected to a parabolic potential confinement, are investigated in the absence of magnetic field. The calculations have been performed by means of the exact diagonalization of the Hamiltonian matrix within the effective-mass approximation. We find that there is only one bound state the D^- center in a spherical parabolic quantum dot in the absence of magnetic field. The binding energy of the ground state is obtained as a function of the dot size. Moreover, the critical confined potential radius value at which the negative donor center changes from unbound to bound is obtained.     

Electric and magnetic field effects on the binding energy of a hydrogenic impurity in quantum well wires with different shapes

In this work, we directly calculate the ground state energies for an electron in quantum well wires (QWWs) with different shapes in the presence of applied electric and magnetic fields using the finite difference method. Then, we study the ground state binding energy of a hydrogenic impurity with a variational approach. We obtain the binding energy for QWWs consisting of the combinations of square and parabolic well potential. Our results indicate that the impurity binding energy depends strongly on the structural confinement and also, on the applied electric and magnetic field.     

Electric field effect on the linear and nonlinear intersubband refractive index changes in asymmetrical semiparabolic and symmetrical parabolic quantum wells

By using the displacement harmonic variant method and the compact density matrix approach, the linear and nonlinear intersubband refractive index changes (RICs) in a semiparabolic quantum well (QW) with applied electric field have been investigated in detail. The simple analytical formulae for the linear and nonlinear RICs in the system were also deduced. The symmetrical parabolic QWs with applied electric fields were taken into account for comparison. Numerical calculations on typical GaAs QWs were performed. The dependence of the linear and nonlinear RICs on the incident optical intensity, the frequencies of the confined potential of the QWs and the strength of the applied electric field were discussed. Results reveal that the RICs in the semiparabolic quantum well system sensitively depend on these factors. The calculation also shows that the semiparabolic QW is a more ideal nonlinear optical system relative to the symmetric parabolic QW systems.     

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.     

The influence of an electric field on a hydrogen atom confined to boxes of different shapes

The ground state energy of a hydrogen atom confined to a box, in the presence of an electric field is calculated. Boxes of various shapes are applied in order to demonstrate the shape's influence on that energy level. The procedure consists of numerically solving the two-dimensional Schrödinger equation using a finite element package.     

Energy Spectra of the Confined Atoms Obtained by Using B-Splines

We have calculated the energy spectra of one- and two-electron atoms (ions) centered in an impenetrable spherical box by variational method with B-splines as basis functions. Accurate results are obtained for both large and small radii of confinement. The critical box radius of confined hydrogen atom is also calculated to show the usefulness of our method. A partial energy degeneracy in confined hydrogen atom is found when the radius of spherical box is equal to the distance at which a node of single-node wavefunctions of free hydrogen atom is located.     

施加电场的半抛物量子阱中束缚态的能级结构

采用位移谐振子与数值求解相结合的方法,研究和讨论了施加电场的半抛物量子阱中束缚态的能级结构,得到了体系的本征能量与本征函数的表达式．数值结果显示,随着电场强度的增大,束缚态的能量几乎线性地下降,电场对半抛物束缚势频率较低的系统以及系统的高能级的影响较大,相邻能级间隔也随着电场强度的增大而减小,这与施加电场的抛物量子阱中的情况明显不同．     

Sum frequency generation in the spherical quantum dots in the presence of applied electric field and spin–orbit interaction

The sum-frequency generation (SFG) is theoretically studied in a quantum dot (QD) through the framework of the effective-mass approximation and compact density matrix approach. QD is spherical with the parabolic potential confinement, under applied electric field and in the presence of Rashba spin-orbit interaction (SOI). Using the computed energies and eigenkets, the second-order susceptibility of SFG has been also calculated as a function of radius of QD, spin–orbit interaction strength and the applied electric field. The effects of Rashba SOI strength, radius of QD and the applied electric field on the second-order of susceptibility coefficient are considered.     

有限深抛物势量子环类氢杂质能级

在有效质量近似下,用微扰法研究InAs量子环内类氢杂质基态及低激发态的能级.受限势采用有限深抛物型势,在二维平面极坐标下,用薛定谔方程的解析解计算.数值结果显示:在抛物势平台区,类氢杂质能级不随电子径向坐标改变,并具有二维氢原子能级的特征;在有限深抛物势区,电子能级敏感地依赖于量子环半径,能级存在极小值,这是由于限制势采用抛物势的结果.如果减小环的半径,可以增加能级间距;简并能级发生分裂并且间距随半径增大而增大,第一激发态的简并没有消除,第二激发态的简并被部分地消除.本文结果对研究量子环的光跃迁及光谱结构有指导意义.     

Nonlinear optical rectification in parabolic quantum dots in the presence of electric and magnetic fields

The optical rectification (OR) coefficient in a parabolic quantum dots (QDs) subject to applied electric and magnetic fields is theoretically investigated in the framework of the compact-density-matrix approach and an iterative method. The confined wave functions and energies of electrons in the QDs are calculated in the effective-mass approximation. Numerical results are presented for typical GaAs/AlGaAs parabolic QDs. These results show that the OR coefficient strongly depends on the radius of QDs and the magnitude of electric and magnetic fields. And the peak shifts to the aspect of high energy when considering the influence of electric and magnetic fields.