环形非球谐振子标量势与矢量势的Klein-Gordon和Dirac方程的束缚态

通过求解环形非球谐振子势的 Klein-Gordon 和 Dirac方程,给出了束缚态波函数与能量方程的精确解,并指出非相对论Schr?dinger方程与具有相等标量势和矢量势的Klein-Gordon 方程以及Dirac方程之间具有数学结构上的等价性。     

Solutions of the Dirac Equation for the Davidson Potential

In the present paper we solve the Dirac equation with Davidson potential by Nikiforov-Uvarov method. The Dirac Hamiltonian contains a scalar S and a vector V Davidson potentials. With equal scalar and vector potential, analytical solutions for bound states of the corresponding Dirac equations are found.     

具有Hulthén的型势的Dirac方程的束缚态

本文给出,具有一维Hulthén型标量势和矢量势的Dirac方程的束缚态精确解。对于三维情况,在Hulthén型标量势和矢量势相等的条件下,给出Dirac方程的S波解。     

Excited states of mesons and the quark-antiquark interaction

The Dirac equation is used in an investigation of the properties of mesons according to the quark-antiquark model. The dependence of the meson mass on angular momentum excitation is considered for several models. The properties of the Dirac equation with a potential consisting of an equal mixture of scalar and vector potential are investigated.     

具有P?schl-Teller型标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态

给出了具P?schl-Teller型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解. 关键词： P?schl-Teller势 Klein-Gordon方程 Dirac方程 束缚态     

一类相对论性非球谐振子系统的束缚态

给出了具有形式为12r²+A2r²的非球谐振子型标量势和矢量势 的相对论系 统在两种势相等的条件下三维Klein-Gordon方程，二维和三维Dirac方程的s波束缚态解. 关键词： 三维非球谐振子势 Klein-Gordon方程 Dirac方程 束缚态     

Wood-Saxon势中相对论粒子的束缚态

给出了具有Wood-Saxon型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解.     

具有Kratzer型标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态

给出了具有Kratzer型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解.     

无反射势阱中相对论粒子的束缚态

给出了具有无反射势型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解. 关键词： 无反射势 Klein-Gordon方程 Dirac方程 束缚态     

具有Morse型标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态

给出了具有Morse型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解. 关键词：     

库仑势加新环形势的相对论束缚态

在标量势等于矢量势的条件下，获得了库仑势加新环形势的Klein-Gordon方程和Dirac方程的束缚态的精确解. 对于Klein-Gordon方程，获得了精确的能谱方程和归一化的波函数. 对于Dirac方程，给出了精确的能谱方程和归一化的旋量波函数. 关键词： 库仑势加新环形势 束缚态 精确解     

Dirac equation with scalar and vector quadratic potentials and Coulomb-like tensor potential

It is shown that the Dirac equation with scalar and vector quadratic potentials and a Coulomb-like tensor potential can be solved exactly. The bound state solutions for equal vector and scalar potentials are obtained. The limit of zero tensor coupling is investigated. The case of equal vector and scalar potentials with opposite sign is also studied. The pseudospin symmetry and its breaking by the tensor interaction are discussed.     

四参数双原子分子势阱中相对论粒子的束缚态

给出了具有四参数双原子分子势型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解. 关键词： 四参数双原子分子势 Klein-Gordon方程 Dirac方程 束缚态     

Dirac equation exact solutions for generalized asymmetrical Hartmann potentials

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of vector and scalar generalized Hartmann potentials. This is done provided the vector potential is equal to or minus the scalar potential. The cases of some quasi-exactly solvable and Morse-like potentials are briefly commented.     

Manning-Rosen标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态

给出了具有Manning-Rosen型标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态解，其解可用超几何函数表示. 关键词： Manning-Rosen势 Klein-Gordon方程 Dirac方程 束缚态     

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.     

第二类Poeschl-Teller势场中相对论粒子的束缚态

给出了具有第二类Poeschl—Teller型标量势与矢量势的Klein-Gordon方程和Dirac方程的8波束缚态解，其解可用超几何函数表示．     

Gap opening in single-layer graphene in the presence of periodic scalar and vector potentials within the continuum model

Gap opening at the Dirac point of the single-layer graphene with periodic scalar and vector potentials has been theoretically investigated under the continuum model. The symmetry analysis indicates that the two-fold degeneracy at the Dirac point can be lifted when the potentials break both the chiral symmetry and the time-reversal symmetry. With the perturbation theory, we derive an analytical expression (gap equation) for gap opening at the Dirac point. Furthermore, the bandgap from the gap equation agrees well with the exact result, when the applied potentials are weak.