The Origin and Mathematical Characteristics of the Super-Universal Associated-Legendre Polynomials

We study the mathematical characteristics of the super-universal associated-Legendre polynomials arising from a kind of double ring-shaped potentials and obtain their polar angular wave functions with certain parity. We find that there exists the even or odd parity for the polar angular wave functions when the parameter η is taken to be positive integer, while there exist both even and odd parities when η is taken as positive non-integer real values. The relations among the super-universal associated-Legendre polynomials, the hypergeometric polynomials, and the Jacobi polynomials are also established.     

The spin-one Duffin Kemmer Petiau equation in the presence of pseudo-harmonic oscillatory ring-shaped potential

The Duffin-Kemmer-Petiau equation （DKP） is studied in the presence of a pseudo-harmonic oscillatory ring-shaped potential in （1 ＋ 3）-dimensional space-time for spin-one particles. The exact energy eigenvalues and the eigenfunctions are obtained using the Nikiforov-Uvarov method.     

Approximate solutions of Dirac equation with a ring-shaped Woods-Saxon potential by Nikiforov-Uvarov method

An approximate analytical solution of the Dirac equation is obtained for the ring-shaped Woods-Saxon potential within the framework of an exponential approximation to the centrifugal term. The radial and angular parts of the equation are solved by the Nikiforov-Uvarov method. The general results obtained in this work can be reduced to the standard forms already present in the literature.     

Solution of Klein-Gordon Equation for Pseudo-Coulomb Potential Plus a New Ring-Shaped Potential

Under the condition of an equal mixing of vector and scalar potentials, exact solutions of bound states of the Klein-Gordon equation with pseudo-Coulomb potential plus a new ring-shaped potential are presented. Simultaneously, energy spectrum equations are also obtained. It is shown that the radial equation and angular wave functions are expressed by confluent hypergeogetric and hypergeogetric functions respectively.     

Influence of temperature on strain-induced polarization Coulomb field scattering in AIN/GaN heterostructure field-effect transistors

Electron mobility scattering mechanism in AlN/GaN heterostuctures is investigated by temperature-dependent Hall measurement, and it is found that longitudinal optical phonon scattering dominates electron mobility near room temperature while the interface roughness scattering becomes the dominant carrier scattering mechanism at low temperatures （~ 100 K）. Based on measured current-voltage characteristics of prepared rectangular AlN/GaN heterostructure field-effect transistor under different temperatures, the temperature-dependent variation of electron mobility under different gate biases is inves- tigated. The polarization Coulomb field （PCF） scattering is found to become an important carrier scattering mechanism after device processing under different temperatures. Moreover, it is found that the PCF scattering is not generated from the thermal stresses, but from the piezoelectric contribution induced by the electrical field in the thin A1N barrier layer. This is attributed to the large lattice mismatch between the extreme thinner AlN barrier layer and GaN, giving rise to a stronger converse piezoelectric effect.     

Temperature Effects of Parabolic Linear Bound Potential and Coulomb Bound Potential Quantum Dot Qubit

On the condition of electric-LO phonon strong coupling in a parabolic quantum dot, we obtain the eigenenergy and the eigenfunctions of the ground state and the first-excited state using the variational method of Pekar type. This system in a quantum dot may be employed as a two-level quantum system-qubit. When the electron is in the superposition state of the ground state and the first-excited state, we obtain the time evolution of the electron density. The relations of the probability density of electron on the temperature and the electron-LO-phonon coupling constant and the relations of the period of oscillation on the temperature, the electron-LO-phonon coupling constant, the Coulomb binding parameter and the confinement length are derived. The results show that the probability density of electron oscillates with a period when the electron is in the superposition state of the ground and the first-excited state, and show that there are different laws that the probability density of electron and the period of oscillation change with the temperature and the electron-LO-phonon coupling constant when the temperature is lower or higher. And it is obtained that the period of oscillation decreases with increasing the Coulomb bound potential and increases with increasing the confinement length not only at lower temperatures but also at higher temperatures.     

Bound states of the SchrSdinger equation for the PSschl-Teller double-ring-shaped Coulomb potential

Poschl-Teller double-ring-shaped Coulomb （PTDRSC） potential, the Coulomb potential surrounded by PSschl- Teller and double-ring-shaped inversed square potential, is put forward. In spherical polar coordinates, PTDRSC potential has supersymmetry and shape invariance in φ,θ and τ coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schr6dinger equation with PTDRSC potential are presented. The normalized φ,θ angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of Laguerre polynomials are presented. Energy spectrum equations are obtained. Wave function and energy spectrum equations of the system are related to three quantum numbers and parameters of PTDRSC potential. The solutions of wave functions and corresponding eigenvalues are only suitable for the PTDRSC potential.     

熔合反应中入射道质量不对成度效应

The symmetric and asymmetric fusion reaction systems forming the same compound nuclei ^26Al, ^30Si, ^38Ar and ^170Hf are investigated with the frame of improved isospin dependent quantum molecular dynamics model. The entrance channel mass asymmetry dependence of compound nucleus formation is found by analyzing the shell correction energies, the Coulomb barriers and the fusion cross sections. The calculated fusion cross sections agree quantitatively with the experimental data. The results indicate that compound nucleus formation is favorable for the systems with larger mass asymmetry because of the smaller Coulomb contribution to the fusion barrier.     

Influence of the channel electric field distribution on the polarization Coulomb field scattering in In0.18Al0.82N/AIN/GaN heterostructure field-effect transistors

By making use of the quasi-two-dimensional （quasi-2D） model, the current-voltage （l-V） characteristics of In0AsA10.82N/A1N/GaN heterostructure field-effect transistors （HFETs） with different gate lengths are simulated based on the measured capacitance-voltage （C-V） characteristics and I-V characteristics. By analyzing the variation of the electron mobility for the two-dimensional electron gas （2DEG） with electric field, it is found that the different polarization charge distributions generated by the different channel electric field distributions can result in different polarization Coulomb field scatterings. The difference between the electron mobilities primarily caused by the polarization Coulomb field scatterings can reach up to 1522.9 cm2/V.s for the prepared In0.38AI0.82N/A1N/GaN HFETs. In addition, when the 2DEG sheet density is modulated by the drain-source bias, the electron mobility presents a peak with the variation of the 2DEG sheet density, the gate length is smaller, and the 2DEG sheet density corresponding to the peak point is higher.     

环形振子势的精确解

将环形振子势的Schrödinger方程在球坐标系中进行变量分离.然后求解了角向方程和径向方程,给出了精确的能谱方程.获得了用普遍的缔合Legendre多项式表示的归一化的角向波函数和用合流超几何函数表示的归一化的径向波函数.     

Path integral treatment of a noncentral electric potential

We present a rigorous path integral treatment of a dynamical system in the axially symmetric potential $V(r,\theta ) = V(r) + \tfrac{1} {{r^2 }}V(\theta ) $ . It is shown that the Green’s function can be calculated in spherical coordinate system for $V(\theta ) = \frac{{\hbar ^2 }} {{2\mu }}\frac{{\gamma + \beta \sin ^2 \theta + \alpha \sin ^4 \theta }} {{\sin ^2 \theta \cos ^2 \theta }} $ . As an illustration, we have chosen the example of a spherical harmonic oscillator and also the Coulomb potential for the radial dependence of this noncentral potential. The ring-shaped oscillator and the Hartmann ring-shaped potential are considered as particular cases. When α = β = γ = 0, the discrete energy spectrum, the normalized wave function of the spherical oscillator and the Coulomb potential of a hydrogen-like ion, for a state of orbital quantum number l ≥ 0, are recovered.     

Exact solutions of the Spinless-Salpeter equation under Kink-Like potential

The exact solution of Spinless-Salpeter equation （SSE） in the presence of Kink-Like potential is in-vestigated. By using the basic concepts of the supersyrnmetric quantum mechanics （SUSYQM） formalism and the functional analysis method, we have obtained the bound state solutions in the closed form and the eigenfunctions of the system are reported in the term of hypergeometric function. We have also reported some numerical results.     

新环状非球谐振子势的Dirac方程束缚态解

提出了一种新的环状非球谐振子势, 在标量势与矢量势相等的条件下, 给出了Dirac 方程的束缚态解.通过分离变量得到Dirac方程相应的角向方程和径向方程,得出了用广义连带勒让德多项式表示的归一化角向波函数和用合流超几何函数表示的归一化径向波函数;获得了精确的束缚态能谱方程并对结果作适当讨论与结论。     

新环状非球谐振子势的Dirac方程束缚态解

提出了一种新的环状非球谐振子势, 在标量势与矢量势相等的条件下, 给出了Dirac 方程的束缚态解.通过分离变量得到Dirac方程相应的角向方程和径向方程,得出了用广义连带勒让德多项式表示的归一化角向波函数和用合流超几何函数表示的归一化径向波函数;获得了精确的束缚态能谱方程并对结果作适当讨论与结论.     

Structural, electronic, and optical properties of ZnOl_xSex alloys using first-principles calculations

The structural, electronic, and optical properties of binary ZnO, ZnSe compounds, and their ternary ZnOl_xSex alloys are computed using the accurate full potential linearized augmented plane wave plus local orbital （FP-LAPW ＋ lo） method in the rocksalt （B 1） and zincblende （B3） crystallographic phases. The electronic band structures, fundamental energy band gaps, and densities of states for ZnO1_xSex are evaluated in the range 0 〈 x 〈 1 using Wu-Cohen （WC） generalized gradient approximation （GGA） for the exchange-correlation potential. Our calculated results of lattice parameters and bulk modulus reveal a nonlinear variation for pseudo-binary and their ternary alloys in both phases and show a considerable deviation from Vegard＇s law. It is observed that the predicted lattice parameter and bulk modulus are in good agreement with the available experimental and theoretical data. We establish that the composition dependence of band gap is semi-metallic in B1 phase, while a direct band gap is observed in B3 phase. The calculated density of states is described by taking into account the contribution of Zn 3d, O 2p, and Se 4s, and the optical properties are studied in terms of dielectric functions, refractive index, reflectivity, and energy loss function for the B3 phase and are compared with the available experimental data.     

Structural,electronic and magnetic properties of the Mn-Ni(110) c(2×2) surface alloy

<正>Using first-principles total energy method,we study the structural,the electronic and the magnetic properties of the MnNi(110) c(2×2) surface alloy.Paramagnetic,ferromagnetic,and antiferromagnetic surfaces in the top layer and the second layer are considered.It turns out that the substitutional alloy in the outermost layer with ferromagnetic surface is the most stable in all cases.The buckling of the Mn-Ni(110) c(2×2) surface alloy in the top layer is as large as 0.26 A(1 A=0.1 nm) and the weak rippling is 0.038 A in the third layer,in excellent agreement with experimental results.It is proved that the magnetism of Mn can stabilize this surface alloy.Electronic structures show a large magnetic splitting for the Mn atom,which is slightly higher than that of Mn-Ni(100) c(2×2) surface alloy(3.41 eV) due to the higher magnetic moment.A large magnetic moment for the Mn atom is predicted to be 3.81μB.We suggest the ferromagnetic order of the Mn moments and the ferromagnetic coupling to the Ni substrate,which confirms the experimental results.The magnetism of Mn is identified as the driving force of the large buckling and the work-function change.The comparison with the other magnetic surface alloys is also presented and some trends are predicted.     

First-principles study of structural,electronic and optical properties of ZnF_2

The structural, electronic, and optical properties of rutile-, CaC12-, and PdF2-ZnF2 are calculated by the plane-wave pseudopotential method within the density functional theory. The calculated equilibrium lattice constants are in reasonable agreement with the available experimental and other calculated results. The band structures show that the rutile-, CaCl2-, and PdF2-ZnF2 are all direct band insulator. The band gaps are 3.63, 3.62, and 3.36 eV, respectively. The contribution of the different bands was analyzed by the density of states. The Mulliken population analysis is performed. A mixture of covalent and weak ionic chemical bonding exists in ZnF2. Furthermore, in order to understand the optical properties of ZnF2, the dielectric function, absorption coefficient, refractive index, electronic energy loss spectroscopy, and optical reflectivity are also performed in the energy range from 0 to 30 eV. It is found that the main absorption parts locate in the UV region for ZnF2. This is the first quantitative theoretical prediction of the electronic and optical properties of ZnF2 compound, and it still awaits experimental confirmation.     

Electronic and Optical Properties of Rock-Salt AIN under High Pressure via First-Principles Analysis

Electronic and optical properties of rock-salt AIN under high pressure are investigated by first -principles method based on the plane-wave basis set. Analysis of band structures suggests that the rock-salt AIN has an indirect gap of 4.53 eV, which is in good agreement with other results. By investigating the effects of pressure on the energy gap, the different movement of conduction band at X point below and above 22.5 GPa is predicted. The optical properties including dielectric function, absorption, reflectivity, and refractive index are also calculated and analyzed. It is found that the rock-salt AIN is transparent from the partially ultra-violet to the visible light area and hardly does the transparence affected by the pressure. Furthermore, the curve of optical spectrum will shift to high energy area （blue shift） with increasing pressure.     

A density functional theory structures,stabilities, and study on size-dependent electronic properties of bimetallic MnAgm （M=Na,Li; n ＋ m ≤ 7） clusters

The equilibrium geometries, relative stabilities, and electronic properties of MnAgm（M=Na, Li; n ＋ m ≤ 7） as well as pure Agn, Nan, Lin （n ≤ 7） clusters are systematically investigated by means of the density functional theory. The optimized geometries reveal that for 2 ≤ n ≤ 7, there are significant similarities in geometry among pure Agn, Nan, and Lin clusters, and the transitions from planar to three-dimensional configurations occur at n = 7, 7, and 6, respectively. In contrast, the first three-dimensional （3D） structures are observed at n ＋ m = 5 for both NanAgm and LinAgm clusters. When n ＋ m ≥5, a striking feature is that the trigonal bipyramid becomes the main subunit of LinAgm. Furthermore, dramatic odd-even alternative behaviours are obtained in the fragmentation energies, secondorder difference energies, highest occupied and lowest unoccupied molecular orbital energy gaps, and chemical hardness for both pure and doped clusters. The analytic results exhibit that clusters with an even electronic configuration （2, 4, 6） possess the weakest chemical reactivity and more enhanced stability.     

Elastic and Thermodynamic Properties of CdSe from First-Principles Calculations

The lattice parameters, bulk modulus, phase transition pressure, and temperature dependencies of the elastic constants cij of CdSe are investigated by using the Cambridge Serial Total Energy Package （CASTEP） program in the frame of Density Functional Theory （DFT）. It is found that the phase transitions from the ZB structure to the RS structure and from WZ structure to RS structure are 2.2 GPa and 2.8 GPa, respectively. Our results agree well with the available experimental data and other theoretical results. The aggregate elastic modulus （B, G, E, A ）, the Poisson＇s ratio （v）, the Griuneisen parameter （γ）, the Debye temperature θD on pressure and temperature are also successfully obtained.