纤锌矿GaN柱形量子点中类氢施主杂质态

在有效质量近似和变分原理的基础上,选取含两个变分参数的波函数,研究了纤锌矿结构的GaN/AlxGa1-xN单量子点中类氢施主杂质体系的结合能随量子点(QD)尺寸以及杂质在量子点中位置的变化,并与以前使用不同尝试波函数的计算结果进行了比较。结果表明:由我们选取的两变分参数波函数得到的结果与前人选取的两变分参数波函数得到的结果相比有所改进,而与选取一个变分参数波函数得到的结果一致。同时我们还计算了体系的维里定理值随量子点半径的变化情况,所得结果与前人工作结果一致,说明本文选取的两变分参数波函数能很好地描述柱形量子点中施主杂质态的运动。     

Variational Principle for a Schrdinger Equation with Non-Hermitian Hamiltonian and Position-Dependent Mass

A classical field theory for a Schrodinger equation with a non-Hermitian Hamiltonian describing a particle with position-dependent mass has been recently advanced by Nobre and Rego-Monteiro(NR)[Phys.Rev.A 88(2013)032105].This field theory is based on a variational principle involving the wavefunction Ψ(x,t) and an auxiliary fieldΦ{x,t).It is here shown that the relation between the dynamics of the auxiliary field Φ(x,t) and that of the original wavefunction Ψ(x,t) is deeper than suggested by the NR approach.Indeed,we formulate a variational principle for the aforementioned Schrodinger equation which is based solely on the wavefunction Ψ(x,t).A continuity equation for an appropriately defined probability density,and the concomitant preservation of the norm,follows from this variational principle via Noether's theorem.Moreover,the norm-conservation law obtained by NR is reinterpreted as tie preservation of the inner product between pairs of solutions of the variable mass Schrodinger equation.     

Excitation of hydrogen atom by positron using hylleraas time-dependent approach

The time-dependent treatment of positron-hydrogen scattering for a zero total angular momentum has been presented. The initial wavefunction of the positron-hydrogen scattering system has been expanded in terms of three dimensional dynamical wave functions to include all higher angular momenta by solving a set of three coupled differential equations. This wavefunction is then time evolved using Taylor series expansion of the evolution operator. The excitation probabilities are monitored as the wavefunction propagates until there is no more change in the probabilities. The positron impact excitation cross-sections extracted from the final wavefunction are compared with the available results of converged close coupling approach. Received 23 July 2001 and Received in final form 25 November 2001     

A new variational calculation for N-dimensional polarons in the strong-coupling limit

A novel variational approach is presented for the calculation of the ground-state energy of the polaron in arbitrary N dimensions in the strong-coupling limit. By using the phonon coherent state to represent the wavefunction of phonons, a self-consistent integro-differential equation for the electron wavefunction is derived. The calculated results of the ground-state energy for N = 1, 2 and 3 agree well with the best results in the literature. It is also found that, for arbitrary N, the present results are less than the Feynman path integral ones by small percentages. It is proposed that this approach should be universal for systems involving polarons in the strong-coupling regime.     

量子反应散射理论及其应用

用交叉分子束和激光技术能够获得从反应物到产物化学变化过程中全部微观的、动态的知识,从而把化学反应动力学发展到基元反应的态态层次.量子反应散射理论能够对自然定律所容许的所有基元双分子态态反应作出最完整的描述.对当前分子反应动力学领域常用的几种量子反应散射理论计算方法,如含时波包传播法,紧耦合微分方程法,散射矩阵变分法及排列通道线性组合散射波函数法的原理及其应用作简单介绍,同时对发展动向作出展望.     

Variable amplitude equations for one-dimensional scattering

Nonlinear first-order equations, similar to Calogero's equations, are derived for the forward and backward one-dimensional scattering amplitudes. In particular, the even potential case yields two uncoupled equations for the even and odd parity phase shifts. The present approach provides a fast and accurate means for the numerical solution of one-dimensional scattering problems. It also has many analytic merits, some of which are discussed. The connection between one-dimensional and three-dimensional high-energy scattering is reviewed. It is demonstrated that in the one-dimensional case, a slightly modified WKB wavefunction provides an excellent approximation to the exact wavefunction in the shortwave limit. In this limit, additivity of phase shifts for nonoverlapping static potentials is satisfied.     

硅中磷塞曼杂化态的波函数混和与组成

报道了硅中磷塞曼（Ｚｅｅｍａｎ）杂化态的波函数混和与组成的直接实验观测结果和理论讨论，用高灵敏度、高分辨率光热电离谱方法定量测量了高纯硅中孤立磷杂质“反相交”（ａｎｔｉ－ｃｒｏｓｓｉｎｇ）塞曼跃迁附近跃迁强度的系统演变，由此导出杂化的束缚杂质电子塞曼能态的波函数组成。用有效质量模型框架下的变分方法计算和讨论了杂化态的波函数组成及相应的跃迁强度，并与实验结果相比较。 关键词：     

Time-Dependent Variational Approach to the Phonon Dispersion Relation of the Commensurate Quantum Frenkel-Kontorova Model

The phonon dispersion relation of the commensurate quantum Frenkel-Kontorova model is studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction for the particles. The single-particle state is taken to be a frozen Jackiw-Kerman wavefunction. Under the condition of minimum uncertainty, equations of motion for the particle expectation values are derived to obtain the phonon dispersion relation. It is shown that the strength of the substrate potential and the phonon excitation gap are reduced due to the quantum fluctuations in comparison with those of the classical model. We also compare our results with those previously obtained by using the path-integral molecular dynamics.     

Incoherent X-ray scattering by atoms in semiclassical approximation

The Fourier transform is used for the evaluation of the semiclassical wavefunction in momentum representation. As a consequence of this approach, the incoherent scattering function is obtained.     

Time-Dependent Variational Approach to Ground-State Phase Transition and Phonon Dispersion Relation of the Quantum Double-Well Model

The ground-state phase transition and the phonon dispersion relation of the quantum double-well model are studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction. The single-particle state is taken to be a frozen Jackiw-Kerman wavefunction. Under the condition of minimum uncertainty relation, we obtain an effective classical Hamiltonian for the system and equations of motion for the particle＇s expectation values. It is shown that the effective substrate potential transits from a symmetric double-well potential to a symmetric single-well potential, and the ground state exhibits a transition from a broken symmetry phase to a restored symmetry phase as increasing the strength of quantum fluctuations. We also obtain the phonon dispersion relations and the phonon gaps at the two phases.     

Binding energy of a screened donor in a spherical quantum dot with a parabolic potential

A wavefunction is proposed for calculating the ground-state energy of a screened donor in a spherical quantum dot under a parabolic potential by a variational method. The donor is taken to be at the center of the quantum dot. Results are presented for four values of the screening parameter by the proposed wavefunction as well as for the hydrogenic donor case by a wavefunction used by Xiao et al.. To assess the accuracy of the results, ‘exact’ energies are also obtained by numerical integration of the Schrödinger equation. It is shown that the proposed wavefunction gives very good results in all cases including the hydrogenic donor case.     

Weighted-Residual Methods for the Solution of Two-Particle Lippmann–Schwinger Equation Without Partial-Wave Decomposition

Recently there has been a growing interest in computational methods for quantum scattering equations that avoid the traditional decomposition of wave functions and scattering amplitudes into partial waves. The aim of the present work is to show that the weighted-residual approach in combination with local basis functions give rise to convenient computational schemes for the solution of the multi-variable integral equations without the partial wave expansion. The weighted-residual approach provides a unifying framework for various variational and degenerate-kernel methods for integral equations of scattering theory. Using a direct-product basis of localized quadratic interpolation polynomials, Galerkin, collocation and Schwinger variational realizations of the weighted-residual approach have been implemented for a model potential. It is demonstrated that, for a given expansion basis, Schwinger variational method exhibits better convergence with basis size than Galerkin and collocation methods. A novel hybrid-collocation method is implemented with promising results as well.     

A Variational Approach for Hadronic Properties in NJL Model

We develop a variational approach for the Nambu-Jona-Lasinio (NJL) model with explicit chiral symmetry breaking and compute the constituent quark mass, the pion decay constant and the vacuum condensate. For a simple ansatz for the hadronic wavefunction, we also analyze the effects of the current quark mass and the ultraviolet cutoff on the static properties of hadrons.     

Simple wavefunction for an impurity in a parabolic quantum dot

A simple variational wavefunction is proposed for calculating the ground-state energy of a hydrogenic donor located at the centre of a spherical parabolic quantum dot. Binding energies are calculated for three values of the parameter which gives the strength of the confining parabolic potential by the proposed wavefunction as well as by a wavefunction used by Xiaoet al. [Superlattices and Microstructures,19, 137 (1996)]. The results are compared to the ‘exact’ energies obtained by numerical integration of the Schrodinger equation. It is shown that the proposed wavefunction gives considerably better results than the wavefunction used by Xiaoet al. in all cases.     

On the applicability of the Lippmann-Schwinger approach to the scattering of particles by semiinfinite crystals

We present a formal approach, using integral equations of the Lippmann-Schwinger type, to the scattering of particles by semiinfinite periodic potentials. The two possible physical situations, scattering of free plane waves and scattering of Bloch waves, are treated with two different integral equations. The validity of this formalism to describe the particle wavefunction in the whole space is established, and its connection with the matching method is studied. The corresponding extinction theorems, one for each situation, are derived. Interesting relations among the probability amplitudes for both scattering problems are found.     

Accurate wavefunctions for hydrogenic donors in GaAs(Ga,Al)As quantum dots

A simple variational wavefunction is proposed for calculating the energy of nodeless quantum states of a hydrogenic donor located at the centre of a spherical GaAs(Ga,Al)As quantum dot. Energies are calculated for the 1s, 2p and 3d states for a range of values of the radius of the quantum dot. The results are compared to the “exact” energies and for the ground state with the results obtained by using the wavefunction proposed by Porras-Montenegro and Perez-Merchancano [Phys. Rev. B 46 (1992) 9780]. For the range of quantum dot radii of practical interest, it is shown that the proposed wavefunction gives results of good accuracy. For the ground state, the results from the proposed wavefunction for R ≤ 4 are considerably better than those obtained from the wavefunction used by Porras-Montenegro and Perez-Merchancano.     

Electronic states of a hydrogenic impurity in a zinc-blende GaN/AlGaN quantum well

Binding energies of ground and a few low lying excited states of a hydrogenic donor confined in a zinc-blende GaN/AlGaN quantum well are investigated. They are computed within the framework of single band effective mass approximation, by means of a variational approach. The donor states are investigated with the various impurity positions as a function of well width. The calculations have been carried out with the inclusion of conduction band non-parabolicity through the energy dependent effective mass. The variational solutions have been improved by using a two-parametric trial wavefunction. The results seem better and good agreement with the other investigators. To support our results, we observe that the values of variational parameters are consistent when two parameter wave function is used. We find that the inclusion of non-parabolic effects leads to more binding for all the values of well width and is significant for narrow wells. The results are compared with the existing available literature.     

Role of the atom-atom scattering length and of symmetrization in unidimensional ultracold atom-diatom collisions

The role of the atom-atom scattering length and of the symmetrization in ultracold atom-diatom collisions in one dimension is presented. For an ultracold atom-diatom collision and for a diatomic molecule in its highest vibrational state, inelastic rate coefficients vanish for a system composed of fermionic atoms as the atom-atom scattering length increases whereas they do not for a system composed of bosonicatoms. The differences come from the symmetrization of the wavefunction of the systems. We explain these differences by comparing the shape of the effective potentials of the atom-diatom approach. For the fermionic system, we use a zero-range interaction to modelize the adiabatic energies and we give a lower estimate of the atom-diatom scattering length as a function of the atom-atom scattering length.     

Variational Monte Carlo analysis of Bose--Einstein condensation in a two-dimensional trap

The ground-state properties of a system with a small number of interacting bosons over a wide range of densities are investigated. The system is confined in a two-dimensional isotropic harmonic trap, where the interaction between bosons is treated as a hard-core potential. By using variational Monte Carlo method, we diagonalize the one-body density matrix of the system to obtain the ground-state energy, condensate wavefunction and the condensate fraction. We find that in the dilute limit the depletion of central condensate in the 2D system is larger than in a 3D system for the same interaction strength; however as the density increases, the depletion at the centre of 2D trap will be equal to or even lower than that at the centre of 3D trap, which is in agreement with the anticipated in Thomas--Fermi approximation. In addition, in the 2D system the total condensate depletion is still larger than in a 3D system for the same scattering length.