中心力问题中的径向期待值及Feynman—Hellman定理

利用Ｆｅｙｎｍａｎ－Ｈｅｌｌｍａｎ（Ｆ－Ｈ）定理，推导了中心力及超中心力问题中径向坐标幂函数的期待值计算公式，并将这些公式应用于Ｋｒａｔｚｅｒ势，修正谐振子势及超球振子势．     

量子系统的能量本征值在超对称性,形状不变性框架下的计算

在超对称性、形产太不变性框架下，计算了一维修正Ｐｏｓｃｈｌ－Ｔｅｌｌｅｒ势、Ｎ维氢原子和Ｎ维各向同性谱振子的能量本征值，得到的能谱公式与用通常的因子化方法得到的严格解完全一致。     

Bi2Sr2—xLaxCaCu2Oy体系正常态热电势的研究

测量了掺Ｌａ的Ｂｉ２２１２系统的随温度变化（８０￣３００Ｋ）的热电势。结果表明，热电势随掺杂浓度的增加（载流子浓度减少）而增大。定性解释了绝样样品的热电势的宽峰移动，并且用Ｎ－Ｌ模型及双带模型对热电势的结果进行了定量分析。     

量子系统的能量本征值在超对称性、形状不变性框架下的计算

在超对称性、形状不变性框架下，计算了一维修正Ｐｓｃｈｌ-Ｔｅｌｅｒ势、Ｎ维氢原子和Ｎ维各向同性谐振子的能量本征值．得到的能谱公式与用通常的因子化方法得到的严格解完全一致 关键词：     

二维钾、钠紫青铜单晶A0.9Mo6O17(A=K,Na)的热电势特性

在８０—２８０Ｋ范围内对准二维钾、钠紫青铜单晶的热电势与温度的关系进行了研究，发现：（１）对钾紫青铜，在１０５Ｋ附近热电势有符号变化，并且在高温正常金属相，热电势Ｓ具有较小的负值，可以用经验关系Ｓ＝ＡＴ＋Ｂ来描述，自由电子为支配载流子；而在Ｔ＜１０５Ｋ的低温ＣＤＷ态，Ｓ为正值，可表示为Ｓ＝Ａ′Ｔ＋Ｂ′／Ｔ的形式，载流子的声子曳引热电势占支配作用．（２）对钠紫青铜，在Ｔ＞８０Ｋ范围内Ｓ与Ｔ具有很好的线性关系，没有观察到Ｐｅｉｅｒｌｓ相变，电子为支配载流子．对造成两者差异的根源，也作了初步探讨 关键词：     

高温下CO2—N2,CO2—CO2混合气体中CO2分子的谱线压力展宽半宽度

用无限阶突变近似方法计算了ＣＯ２－Ｎ２,ＣＯ２－ＣＯ２混合气体中Ｃ承２９６－１９２９Ｋ温度下转动量子数从１到３０的谱线压力展宽半宽度。计算过程中各系统的相互作用势采用改进的Ｂｕｃｋｉｎｇｈａｍ模型势。得到的结果和现有结果符合较好。     

具有Kratzer势的N维Schrdinger方程的束缚态精确解

精确地求解了具有Kratzer势的N(N≥ 2 )维束缚态Schr dinger方程 ,给出了具有Kratzer势的N维双原子分子的能级及相应的归一化径向波函数     

二维旋转简谐振子势的讨论

以二维旋转简谐振子势为例分析了在BEC中经常用到的旋转势,分析了哈密顿量的表达式,给出了波函数和能量本征值,并注意到了二维旋转简谐振子势与带电粒子在磁场中的情形具有相近的形式.     

掺杂KNSBN晶体吸收对光强的依赖特性

研究了Ｃｏ：ＫＮＳＢＮ晶体和重还原Ｃｏ：ＫＮＳＢＮ晶体中光致吸收的变化特性。Ｃｏ：ＫＮＳＢＮ晶体的吸收系数随泵浦光强的增加而减小，吸收系数变化的最大值为３．２ｃｍ＾－１，重还原Ｃｏ：ＫＮＳＢＮ的吸收系数随泵浦光强的增加而增加，吸收系数变化的最大值为６．５ｃｍ＾－１，在泵浦光关掉后，探测光频率很高的增幅振荡，然后呈现阻尼振荡，采用最近建立的双载流子（电子，空穴）和多重陷阱能级（两个深陷阱能级，两个浅     

2N+1阶KdV型方程的孤波解

获得了２Ｎ＋１阶ＫｄＶ型方程的显式精确孤波解．作为特例，讨论了高阶广义ＫｄＶ型方程、高阶广义ＭＫｄＶ型方程和高阶广义Ｓｃｈａｍｅｌ的ＭＫｄＶ型方程．还研究了２Ｎ＋１阶ＫＰ型方程 关键词：     

Solution of the Dirac Equation for Ring-Shaped Modified Kratzer Potential

We propose a new exactly solvable potential which is Formed by modified Kratzer potential plus a new ring-shaped potential η cot^2 θ/r^2 The solutions of the Dirac equation with equal scalar and vector ring-shaped modified Kratzer potential are found by using the Nikiforov-Uvarov method. The nonrelativistic limit of the energy spectrum has been discussed.     

Effective Kratzer and Coulomb potentials as limit cases of a multiparameter exponential-type potential

We show that the effective Kratzer and Coulomb potentials can be obtained by taking particular limits of a multiparameter exponential potential that was studied recently. Moreover, we demonstrate that the bound state solutions of the exponential potential reduce correctly to their well-known counterparts associated with the Kratzer and Coulomb potentials. As a byproduct, we obtain a new limit relation for the hypergeometric function.     

AIM Solutions to the DKP Equation for Spin-1 Particles in the Presence of Kratzer Potential in (2+1) Dimensions

The relativistic Duffin–Kemmer–Petiau equation for spin-1 particles in the presence of the Kratzer potential is studied analytically within the framework of the asymptotic iteration method. The exact energy eigenvalues and corresponding eigenfunctions of spin-1 particles are obtained for arbitrary quantum states by solving the Duffin–Kemmer–Petiau equation with Kratzer potential.     

The Supersymmetry Approaches to the Non-central Kratzer Plus Ring-Shaped Potential

In this paper, we study the Schr?dinger equation with non-central modified Kratzer potential plus a ring-shaped like potential, which is not spherically symmetric. We connect the corresponding Schr?dinger equation to the Laguerre and Jacobi equations. These lead us to have some raising and lowering operators which are first order equations. We take advantage from these first order equations and discuss the supersymmetry algebra. And also we obtain the corresponding partner Hamiltonian for Kratzer potential and investigate the commutation relation for the generators algebra.     

Splitting of Spectra in Anharmonic Oscillators Described by Kratzer Potential Function

A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonie model of a two-dimensional oscillator having Kratzer potential energy function is used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interaction between the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a reaJ polyatomic molecular species.     

Core/shell/shell spherical quantum dot with Kratzer confining potential: Impurity states and electrostatic multipoles

An exactly solvable problem of impurity states is considered in core/shell/shell spherical quantum dot. Kratzer molecular potential is taken for confinement potential. The analytical expressions are obtained for the energy spectrum and wave functions of the impurity electron. The dependencies of the total energy and the binding energy of the impurity on the parameters of the confining potential are investigated. The possibility of the impurity electron leakage is shown in the external environment, due to the specific form of the Kratzer potential. The character of the electrostatic field created by the impurity and the electron is observed on the basis of obtained results. The multipole corrections caused by the dipole and quadrupole moments of the electron are calculated. It is shown that the dipole moment is absent, and the problem reduces to the calculation of only z component for the average values of the diagonal elements of the quadrupole moment tensor. The dependencies of the average values of the quadrupole moment on the Kratzer potential parameters are studied.     

Mapping of Shape Invariant Potentials by the Point Canonical Transformation

In this paper by using the method of point canonical transformation we find that the Coulomb and Kratzer potentials can be mapped to the Morse potential. Then we show that the Pöschl-Teller potential type I belongs to the same subclass of shape invariant potentials as Hulthén potential. Also we show that the shape-invariant algebra for Coulomb, Kratzer, and Morse potentials is SU(1,1), while the shape-invariant algebra for Pöschl-Teller type I and Hulthén is SU(2).     

The energy eigenvalues of the Kratzer potential in the presence of a magnetic field

Two dimensional solution of the Schr?dinger equation for the Kratzer potential with and without the presence of a constant magnetic field is investigated within the framework of the asymptotic iteration method. The energy eigenvalues are analytically obtained for the absence of the magnetic field case. However, in the presence of a constant magnetic field, the energy eigenvalues are calculated numerically using the same method. The results obtained by using different Larmor frequencies and potential parameters are compared with the results of the absence of the magnetic field case (ω _L = 0). Effect of the magnetic field on the energy eigenvalues of the Kratzer potential is precisely presented.     

Exact Solutions to Three-Dimensional Schrödinger Equation with an Exponentially Position-Dependent Mass

For an exponentially position-dependent mass, we obtain the exact solutions of the three-dimensional Schrödinger equation by using coordinate transformation method for the reference problems with Coulomb potential, Kratzer potential, and spherically square potential well of infinite depth, respectively. The explicit expressions for the energy eigenvalues and the corresponding eigenfunctions of the three systems are presented.     

Exact solutions of spin-one DKP equation under Kratzer potential in (1 + 2) dimensions

We study the relativistic spin-one Duffin-Kemmer-Petiau equation in the presence of Kratzer potential in (1 + 2)-dimensional Minkowski space-time. To obtain the energy eigenvalues and the corresponding eigenfunctions, the analytical Nikiforov-Uvarov method is used.