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

给出了具有Poschl-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.     

Supersymmetry and Solution of Dirac Equation with Vector and Scalar Potentials

The Dirac equations with vector and scalar potentials of the Coulomb types in two and three dimensions are solved using the supersymmetric quantum mechanics method. For the system of such potentials, the analytical expressions of the matrix dements for both position and momentum operators are obtained.     

Dirac Equation for Scalar,Vector and Tensor Generalized Cornell Interaction

We consider spin and pseudospin symmetry limits of Dirac equation in the presence of scalar, vector and tensor generalized Cornell interaction and report the solutions via the quasi-exact analytical ansatz approach.     

Interacting random Dirac fermions in superconducting cuprates

We study the effects of quasiparticle interactions on disorder-induced localization of Dirac-like nodal excitations in superconducting high- Tc cuprates. As suggested by the experimental angle-resolved photoemission spectroscopy and terahertz conductivity data in Bi2Sr2CaCu2O(8+delta), we focus on the interactions mediated by the order parameter fluctuations near an incipient second pairing transition d --> d + is(id'). We find interaction corrections to the density of states, specific heat, and conductivity as well as phase and energy relaxation rates and assess the applicability of the recent localization scenarios for noninteracting random Dirac fermions to the cuprates.     

Interacting Gravitational and Dirac Fields with Torsion

A general interaction scheme is formulated in a general space–time with torsion from the action principle by considering the gravitational, the Dirac, and the torsion field as independent fields. Some components of the torsion field come out to be automatically zero. Both the resulting Einstein-like and the Dirac-like fields equations contain nonlinear terms given by a self-interaction of the Dirac spinor and originally produced by torsion. The theory is specialized to the Robertson–Walker space–time without torsion. To solve he corresponding equations, that still have a complex structure, the spin coefficients have to be calculated explicitly from the tetrad employed. A solution, even if simple and elementary, is then determined.     

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.     

Complex Geometry and Dirac Equation

Complex geometry represents a fundamentalingredient in the formulation of the Dirac equation bythe Clifford algebra. The choice of appropriate complexgeometries is strictly related to the geometricinterpretation of the complex imaginary unit . We discuss two possibilities which appearin the multivector algebra approach: the₁₂₃ and ₂₁ complexgeometries. Our formalism provides a set of rules which allows an immediate translation between thecomplex standard Dirac theory and its version withingeometric algebra. The problem concerning a doublegeometric interpretation for the complex imaginary unit is also discussed.     

Quaternion Dirac Equation and Supersymmetry

Quaternion Dirac equation has been analyzed and its supersymmetrization has been discussed consistently. It has been shown that the quaternion Dirac equation automatically describes the spin structure with its spin up and spin down components of two component quaternion Dirac spinors associated with positive and negative energies. It has also been shown that the supersymmetrization of quaternion Dirac equation works well for different cases associated with zero mass, nonzero mass, scalar potential and generalized electromagnetic potentials. Accordingly we have discussed the splitting of supersymmetrized Dirac equation in terms of electric and magnetic fields.     

Dirac Equation at Finite Temperature

In this paper, we propose finite temperature Dirac equation, which can describe the quantum systems in an arbitrary temperature for a relativistic particle of spin-1/2. When the temperature T=0, it become Dirac equation. With the equation, we can study the relativistic quantum systems in an arbitrary temperature.     

A Search on Dirac Equation

The solutions, in terms of orthogonal polynomials, of Dirac equation with analytically solvable potentials are investigated within a novel formalism by transforming the relativistic equation into a Schrodinger-like one. Earlier results are discussed in a unified framework, and some solutions of a large class of potentials are given.     

The Geometry of the Dirac Equation

We discuss the problem of the derivation and the interpretation of metric tensors and generalized equations of motion for test particles from quasilinear spinor equations.     

An Ansatz Solution of Dirac Equation under Scalar and Vector Soft-Core Coulomb and Coulomb Tensor Interactions

We study Dirac equation for scalar and vector soft-core Coulomb potentials and a Tensor Coulomb term in spin and pseudospin symmetries via the quasi-analytical ansatz technique.     

Exactly Solvable Combinations of Scalar and Vector Potentials for the Dirac Equation Interrelated by Riccati Equations

New classes of solvable scalar and vector potentials for the Dirac equation are obtained, together with the associated exact Dirac spinors. The method of derivation is based on an a priori constraint between the solutions, leading to an interrelation between the scalar and vector potential in the form ofa Riccati equation. The present note generalizes a series of former articles.     

Dirac–Kähler Equation

Tensor, matrix, and quaternion formulations of Dirac–Kähler equation for massive and massless fields are considered. The equation matrices obtained are simple linear combinations of matrix elements in the 16-dimensional space. The projection matrix-dyads defining all the 16 independent equation solutions are found. A method of computing the traces of 16-dimensional Petiau–Duffin–Kemmer matrix product is considered. We show that the symmetry group of the Dirac–Kähler tensor fields for charged particles is SO(4, 2). The conservation currents corresponding this symmetry are constructed. We analyze transformations of the Lorentz group and quaternion fields. Supersymmetry of the Dirac–Kähler fields with tensor and spinor parameters is investigated. We show the possibility of constructing a gauge model of interacting Dirac–Kähler fields where the gauge group is the noncompact group under consideration.     

Time Delay for the Dirac Equation

We consider time delay for the Dirac equation. A new method to calculate the asymptotics of the expectation values of the operator \({\int\limits_{0} ^{\infty}{\rm e}^{iH_{0}t}\zeta(\frac{\vert x\vert }{R}) {\rm e}^{-iH_{0}t}{\rm d}t}\), as \({R \rightarrow \infty}\), is presented. Here, H₀ is the free Dirac operator and \({\zeta\left(t\right)}\) is such that \({\zeta\left(t\right) = 1}\) for \({0 \leq t \leq 1}\) and \({\zeta\left(t\right) = 0}\) for \({t > 1}\). This approach allows us to obtain the time delay operator \({\delta \mathcal{T}\left(f\right)}\) for initial states f in \({\mathcal{H} _{2}^{3/2+\varepsilon}(\mathbb{R}^{3};\mathbb{C}^{4})}\), \({\varepsilon > 0}\), the Sobolev space of order \({3/2+\varepsilon}\) and weight 2. The relation between the time delay operator \({\delta\mathcal{T}\left(f\right)}\) and the Eisenbud–Wigner time delay operator is given. In addition, the relation between the averaged time delay and the spectral shift function is presented.     

The Dirac Equation in Binary Geometrophysics

Within the framework of a program of the construction (derivation) of the classical space-time from a certain system of notions and relations (binary systems of complex relations) that show up in microcosm physics, the prototype of the Dirac equation for a free particle is considered, and the change from this prototype to the Dirac equation is followed first in the momentum and then in the coordinate representation. The procedure of changing from elementary bases to a macroinstrument in reference to which the generally accepted physical notions are formulated.     

Quaternionic Lorentz Group and Dirac Equation

We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time transformations, we combine these one-dimensional spinors into bi-dimensional column vectors. From the transformation properties of the two-component spinors, we derive a quaternionic chiral representation for the space-time algebra. Finally, we obtain a quaternionic bi-dimensional version of the Dirac equation.     

Coulomb-Like Interactions in the Dirac Equation

The Dirac equation for the Coulomb-like problem is modified by incorporating minimal interactions into the Dirac Hamiltonian, that keep the 1/r potential dependence. We determine the general energy eigenvalues and the corresponding eigenfunctions.     

Some Studies of the Neutron's Dirac Equation

In this paper, we continue the discussion for the neutron's Dirac equation and relevant problems after Ref.[1]. We consider the neutron's Dirac equation with the electric moment besides the magnetic moment, solve rigorously the neutron's Dirac equation in a uniform electromagnetic field. We also set up a relativistic neutron's spin-echo theory with a magnetic moment.