二维环状δ势的束缚态

讨论了二维自由空间和各向同性谐振子势下环状δ势束缚态波函数的表示,发现波函数由合流超几何函数和屈科米函数表示.由波函数在边界的衔接条件,得到了能谱方程,并给出了一定条件下前5个能级的数值解.     

一类环状非球谐振子势场中相对论粒子的束缚态解

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，给出了其Klein-Gordon方程和Dirac方程的束缚态解. Klein-Gordon方程的θ角向波函数以超几何函数表示，径向波函数可用合流超几何函数或广义拉盖尔多项式表示，能谱方程由径向波函数满足的束缚态边界条件得到. Dirac方程的旋量波函数可用Klein-Gordon方程的解构造. 关键词： 环状非球谐振子势 Klein-Gordon方程 Dirac方程 束缚态     

环形非球谐振子势Klein-Gordon方程的束缚态

用分离变量方法讨论了在环形非球谐振子标量势和矢量势相等条件下的Klein-Gordon方程的束缚态解.给出了用广义连带勒让得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. 关键词： 环形非球谐振子势 Klein-Gordon方程 束缚态     

一种简捷求解定态薛定谔方程的方法:科尔-霍普夫变换法

介绍一种求解各个能级及定态波函数的简捷方法,即借助于科尔-霍普夫(Cole-Hopf)变换法,将给定势函数的定态薛定谔方程变换成黎卡提(Riccati)方程,以求出各个能级及定态波函数.并以谐振子、球谐振子、氢原子、P schl-Teller势、Morse势、Hulth啨n势、双原子分子的三参量势函数、同调谐振子为实例,给出求解方法及结果.     

类Quesne环状球谐振子势场中的赝自旋对称性

提出了一种新的类Quesne环状球谐振子势,应用二分量方法求解1/2-自旋粒子满足的Dirac方程, Dirac哈密顿量由标量和矢量类Quesne环状球谐振子势构成.在Σ=S(r)+V(r)=0的条件下,得到了Dirac旋量波函数下分量的束缚态解和能谱方程, 显示出类Quesne环状球谐振子势场中的赝自旋对称性.讨论了束缚态波函数和能谱方程的有关性质. 关键词： 类Quesne环状球谐振子势 Dirac方程 赝自旋对称性 束缚态     

非球谐振子势Schr(o)dinger方程的精确解

将非球谐振子势V(r)=ar2+br4+cr6径向波函数展开为指数函数与多项式函数的乘积,应用多项式函数的系数关系确定了体系的能级和波函数.结果表明,体系处于束缚态时,势参数a,b,c必须满足一定的约束条件.     

势场作用下粒子的双缝干涉现象分析

根据费曼路径积分原理,定量分析了势场作用下粒子的双缝干涉实验,分别得到谐振子势和线性势下粒子的干涉强度分布公式,并对两种势场下的干涉条纹作了分析.指出谐振子势下粒子的双缝干涉受势场角频率控制,线性势下干涉条纹主极大发生位移.最后,由路径积分的计算过程分析得知,双缝的形状决定强度分布公式,与波动光学的分析结果一致.     

非球谐振子势Schrdinger方程的精确解

将非球谐振子势V(r) =ar2 br4 cr6 径向波函数展开为指数函数与多项式函数的乘积 ,应用多项式函数的系数关系确定了体系的能级和波函数 .结果表明 ,体系处于束缚态时 ,势参数a ,b ,c必须满足一定的约束条件     

研究量子耗散配分函数的变分数值方法

提出了用变分路径各分方法一子耦散系统的配分函数。将势能和耦合函数分别写成谐振子势和线性函数与剩余项之和。其中所引入的两个试探函数Ω＾２和μ（ｘ０）由有效势取极不小值的条件所确定。     

一类非谐振模型势径向平均值的解析表达式及其递推关系

获得了一类非谐振模型势，即环形非球谐振子、非球谐振子和环形振子径向平均值的两个递推关系.给出了这些非谐振模型势的部分径向幂次平均值的解析表达式. 关键词： 环形非球谐振子 非球谐振子 环形振子 径向平均值 解析表达式 递推关系     

A New Type of Shape-Invariant Potential

It has been shown that Hulthen potental and isotonic harmonic oscillator potential are shape-invariant potentials with a translation of parameters, and isotonic harmonic oscillator potential and three-dimensional harmonic oscillator potential belong to a type of shape-invariant potentials.     

Optical rectification coefficient in an oxide quantum dot with different confinement potentials

Exciton binding energies, oscillator strength, optical rectification coefficients and second harmonic generation are investigated using three different confinement potentials in a CdO/ZnO core/shell quantum dot. The bare potential, Smorodinsky–Winternitz potential and Woods–Saxon potential are employed in the Hamiltonian. The position dependent dielectric function is used. The electronic properties are found using variational formulism within a single band effective mass approximation whereas the optic properties are investigated using compact density matrix approach. The results show that different confinement potentials lead to significant changes in the coefficients of optical rectification and the second harmonic generations and the effects of confined potentials are more pronounced in the strong confinement region. The resonant peaks in the nonlinear optical rectification coefficients and second harmonic generation are blue shifted to larger photon energies with the various confined potentials and the results are enhanced using Smorodinsky–Winternitz potential. The obtained results can be applied for the potential applications for fabricating opto-electronic devices.     

具有含时平方反比项的谐振子的路径积分求解

使用含时坐标变换把一个质量含时的带有平方反比项的谐振子系统变换为对应的质量不含时 谐振子系统.利用变换前、后传播子之间的关系并通过Feynman路径积分的方法求出质量含时 的带有平方反比项的谐振子系统的传播子与精确波函数.并对包含有更多的附加势的谐振子 系统进行了讨论. 关键词： 谐振子 坐标变换 路径积分 传播子     

Pseudospin Symmetry for a Ring-Shaped Non-spherical Harmonic Oscillator Potential

The pseudospin symmetry for a ring-shaped non-spherical harmonic oscillator potential is investigated by solving the Dirac equation with equal mixture of scalar and vector potentials with opposite signs. The normalized spinor wave function and energy equation are obtained, the algebraic property of the energy equation and some particular cases are also discussed.     

Pseudospin symmetry and a double ring-shaped spherical harmonic oscillator potential

A new double ring-shaped spherical harmonic oscillator potential is presented. The pseudospin symmetry in this system is investigated by solving the Dirac equation with equal mixture of scalar and vector potentials with opposite signs. The normalized spinor wave function and energy equation are obtained and some particular cases are discussed.      

Pseudospin symmetry and the relativistic ring-shaped non-spherical harmonic oscillator

A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The eigenfunctions and eigenenergies are obtained for the ring-shaped non-spherical harmonic oscillator by solving Dirac equation with equal mixture of vector and scalar potentials in opposite signs, for which pseudospin symmetry is exact. Several particular cases such as the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed.     

The relativistic bound states for a new ring-shaped harmonic oscillator

In this paper a new ring-shaped harmonic oscillator for spin 1/2 particles is studied, and the corresponding eigenfunctions and eigenenergies are obtained by solving the Dirac equation with equal mixture of vector and scalar potentials. Several particular cases such as the ring-shaped non-spherical harmonic oscillator, the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed.     

High energy behaviour of the scattering amplitude in the presence of confined channels

The two-channel potential scattering problem in three space-dimensions is considered in the case when one channel is permanently confined. Two examples of confining potentials are considered: the harmonic oscillator and the infinite well. The two cases give radically different results: for the infinite well there is no high-energy limit; in the case of the harmonic oscillator the amplitude has properties similar to that of dual absorptive models.     

Darboux transformation and elementary exact solutions of the Schrödinger equation

Darboux transformation is applied to three classical potentials, namely the harmonic oscillator, effective Coulomb and Morse potentials to generate exactly solvable potentials of elementary form. For every potential, the isospectral families of potentials are constructed. For almost all potentials, a set of normalized discrete spectrum wave functions is given.