First attempt to overcome the disaster of Dirac sea in imaginary time step method

Efforts have been made to solve the Dirac equation with axially deformed scalar and vector Woods-Saxon potentials in the coordinate space with the imaginary time step method. The results of the single-particle energies thus obtained are consistent with those calculated with the basis expansion method, which demonstrates the feasibility of the imaginary time step method for the relativistic static problems.     

Woods-Saxon势下的赝自旋对称性

通过求解具有Woods-Saxon径向标量势与矢量势的Dirac方程, 分别分析了原子核中赝自旋双重态能级劈裂和波函数下分量劈裂随着Woods-Saxon势参数的变化关系, 其中Wood-Saxon势中的参数a以及R对于赝自旋能级劈裂和波函数劈裂的影响最大, 而势阱深度V₀只产生微小的影响. 随着平均场的变化, 赝自旋双重态会出现能级反转现象. 具有较大n或l的赝自旋双重态能级劈裂对于参数的变化更敏感. 赝自旋波函数下分量劈裂随着参数a和R的增大向核表面扩散, 并且在核表面附近达到最大. 赝自旋波函数劈裂随着参数a的增大而增大, 但是随着参数R或V₀的增大它却在减小的. 由于在特定的同位素链中, 参数R和V₀都与核子数有关系, 而参数a又是描述核的表面性质的, 所以以这些参数为变量对于赝自旋劈裂的研究是有意义的, 研究的结果至少在定性上可以应用到大部分原子核中.     

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.     

Exact solution to the one-dimensional Dirac equation of linear potential

In this paper the one-dimensional Dirac equation with linear potential has been solved by the method of canonical transformation. The bound-state wavefunctions and the corresponding energy spectrum have been obtained for all bound states.     

Makarov势的Dirac方程的束缚态解

给出了Makarov型标量势与矢量势相等条件下的Dirac方程的束缚态解. Dirac方程的角向方程用因子分解方法求解，在得出角向波函数的过程中，自然地得到了属于同一本征值的不同角向波函数间的递推操作. 径向束缚态波函数用合流超几何函数表示，束缚态的能量方程可由径向波函数满足的边界条件得到. 关键词： Makarov势 Dirac方程 束缚态 因子分解方法     

Bound states of the Dirac equation with position-dependent mass for the Eckart potential

Studying with the asymptotic iteration method, we present approximate solutions of the Dirac equation for the Eckart potential in the case of position-dependent mass. The centrifugal term is approximated by an exponential form, and the relativistic energy spectrum and the normalized eigenfunctions are obtained explicitly.     

Exact pseudospin symmetry solution of the Dirac equation for spatially-dependent mass Coulomb potential including a Coulomb-like tensor interaction via asymptotic iteration method

In this Letter, the Dirac equation is exactly solved for spatially-dependent mass Coulomb potential including a Coulomb-like tensor potential under pseudospin symmetry limit by using asymptotic iteration method with arbitrary spin-orbit coupling number κ. The energy eigenvalues and corresponding eigenfunctions are obtained and some numerical results are given.     

Approximate any 1-state solutions of the Dirac equation for modified deformed Hylleraas potential by using the Nikiforov-Uvarov method

<正>We investigate the spin and pseudospin symmetries of the Dirac equation under modified deformed Hylleraas potential via a Pekeris approximation and the Nikiforov-Uvarov technique.A tensor interaction of Coulomb form is considered and its degeneracy-removing role is discussed in detail.The solutions are reported for an arbitrary quantum number in a compact form and useful numerical data are included.     

Two-Dimensional Linear Dependencies on the Coordinate Time-Dependent Interaction in Relativistic Non-Commutative Phase Space

In this paper, the Non-Commutative phase space and Dirac equation, time-dependent Dirac oscillator are introduced. After presenting the desire general form of a two-dimensional linear dependency on the coordinate time-dependent potential, the Dirac equation is written in terms of Non-Commutative phase space parameters and solved in a general form by using Lewis-Riesenfield invariant method and the time-dependent invariant of Dirac equation with two-dimensional linear dependency on the coordinate time-dependent potential in Non-Commutative phase space has been constructed, then such latter operations are done for time-dependent Dirac oscillator. In order to solve the differential equation of wave function time evolution for Dirac equation and time-dependent Dirac oscillator which are partial differential equation some appropriate ordinary physical problems have been studied and at the end the interesting result has been achieved.     

Approximate Analytical Solutions of the Dirac Equation with the Hyperbolic Potential in the Presence of the Spin Symmetry and Pseudo-spin Symmetry

By employing a new improved approximation scheme to deal with the centrifugal term and pseudo-centrifugal term, we solve approximately the Dirac equation with the hyperbolic potential for the arbitrary spin-orbit quantum number κ. Under the condition of the spin and pseudospin symmetry, the bound state energy eigenvalues and the associated two-component spinors of the Dirac particle are obtained approximately by using the basic concept of the supersymmetric shape invariance formalism and the function analysis method.     

Dirac bound states of anharmonic oscillator in external fields

We explore the effect of the external magnetic and Aharonov–Bohm (AB) flux fields on the energy levels of Dirac particle subjects to mixed scalar and vector anharmonic oscillator field in the two-dimensional (2D) space. We calculate the exact energy eigenvalues and the corresponding un-normalized two-spinor-components wave functions in terms of the chemical potential parameter, magnetic field strength, AB flux field and magnetic quantum number by using the Nikiforov–Uvarov (NU) method.     

Exact solutions of Dirac equation with Pöschl–Teller double-ring-shaped Coulomb potential via Nikiforov–Uvarov method

Exact analytical solutions of the Dirac equation are reported for the Pöschl-Teller double-ring-shaped Coulomb potential. The radial, polar, and azimuthal parts of the Dirac equation are solved by using the Nikiforov-Uvarov method, and exact bound state energy eigenvalues and the corresponding two-component spinor wavefunctions are reported.     

Relativistic symmetries in the Rosen-Morse potential and tensor interaction using the Nikiforov-Uvarov method

Approximate analytical bound-state solutions of the Dirac particle in the fields of attractive and repulsive Rosen- Morse (RM) potentials including the Coulomb-like tensor (CLT) potential are obtained for arbitrary spin-orbit quantum number κ. The Pekeris approximation is used to deal with the spin-orbit coupling terms κ(κ± 1)r 2 . In the presence of exact spin and pseudospin (p-spin) symmetries, the energy eigenvalues and the corresponding normalized two-component wave functions are found by using the parametric generalization of the Nikiforov-Uvarov (NU) method. The numerical results show that the CLT interaction removes degeneracies between the spin and p-spin state doublets.     

伪自旋对称情形下Rosen-Morse类型势场中相对论粒子的束缚态

在伪自旋对称情形下研究了Rosen-Morse类型势场中相对论粒子的束缚态,利用Nikiforov-Uvarov方法求解了伪自旋对称情形下的Klein-Gordon和Dirac方程,得到了相对论粒子被束缚在Rosen-Morse类型势场的精确束缚态解.     

时域小波Galerkin法在有耗地面与任意目标复合散射中的应用

采用时域小波Galerkin(WGTD)方法计算了有耗地面与三维目标的复合散射,其中连接边界采用三波法.得到近场数据后,为避免复杂的Sommerfeld积分用互易原理简化了外推过程.计算了地面目标的雷达散射截面,验证了WGTD方法的精度和有效性.与时域有限差分方法相比,WGTD方法具有色散线性好、节省内存、计算速度快等优点. 关键词： 时域小波Galerkin法 复合散射 有耗半空间     

一种计算分层半空间上方导线瞬态响应的新方法

提出了一种将时域积分方程(time domain integral equation, TDIE)方法和时域有限差分(finite differnce time domain, FDTD)方法相结合计算分层有耗半空间上方导线瞬态电磁响应的新方法.其中,一维FDTD方法用于计算入射电磁波经分层半空间反射的时域波形.TDIE用于求解细导线在加入两个激励源(直接入射电磁波和经分层半空间反射的电磁波)时的瞬态响应.相关计算理论和数值模拟结果说明了本文方法是一种解决了分层有耗介质上方水平放置导线瞬态响应的高效解决方案. 关键词： 时域积分方程 时域有限差分 细导线 分层半空间     

用落球法测液体粘度计时起点的确定

根据斯托克斯定律和牛顿第二定律导出了小球到达终极速度半,小球的运动距离与速度之间的函数关系,从理论上对计时起点的确定给予了证明,并讨论了小球半径的合理取值。     

Solutions of the Duffin-Kemmer-Petiau equation in the presence of Hulthn potential in(1+2) dimensions for unity spin particles using the asymptotic iteration method

The relativistic Duffin-Kemmer-Petiau equation in the presence of Hulthn potential in(1+2) dimensions for spin-one particles is studied.Hence,the asymptotic iteration method is used for obtaining energy eigenvalues and eigenfunctions.