相关论文: The Strong Levinson Theorem for the Dirac Equation

This paper deals with the relativistic, quantized electromagnetic and Dirac field equations in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. In the consequent…

The purpose of this comment is to clarify two points related to the Dirac equation. First, the Lorentz structure of the potential and its connection with the Klein paradox. Second, the connection between the number of space dimensions and…

Dirac's idea of taking the square root of constraints is applied to the case of extended objects concentrating on membranes in D=4 space-time dimensions. The resulting equation is Lorentz invariant and predicts an infinite hierarchy of…

We present a new approach to study (1+1)-dimensional Dirac equation in the background of an effective mass $M$ by exploiting the possibility of a position-dependent fermi velocity $v_f$. We explore the resulting structure of the coupled…

Dirac equation for a charged particle in static electromagnetic field is written for special cases of spherically symmetric potentials. Besides the well known Dirac-Coulomb and Dirac-Oscillator potentials, we obtain a relativistic version…

We find an exact solution to the Dirac equation in 1-1 dimensional space-time in the presence of a time-dependent potential which consists of a combination of electric, scalar, and pseudoscalar terms.

The Dirac equation is used to describe oblique spin-conserving and spin-flip reflections of relativistic electrons from a one-dimensional potential barrier in a vacuum. When an electron hits the barrier from an oblique direction, its…

We obtain an exact solution of the Dirac equation in (2+1)-dimensions in the presence of a constant magnetic field normal to the plane together with a two-dimensional Dirac-oscillator potential coupling. The solution space consists of a…

In quantum scattering theory, there exists a relationship between the difference in the scattering phase shifts at threshold and infinity and the number of bound states, which is established by the Levinson theorem. The presence of…

The Dirac equation with a U(1) vortex in the mass-term is solved in the presence of magnetic-like fields at zero energy. By drawing an analogy to classical mechanics, it is shown that the four-component Dirac equation in arbitrary magnetic…

We show how the scattering phase shift, the s-wave scattering length and the p-wave scattering volume can be obtained from Riccati equations derived in variable phase theory. We find general expressions that provide upper and lower bounds…

In the light of the Sturm-Liouville theorem, the Levinson theorem for the Schr\"{o}dinger equation with both local and non-local cylindrically symmetric potentials is studied. It is proved that the two-dimensional Levinson theorem holds for…

A self-contained discussion of integral equations of scattering is presented in the case of centrally-symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and…

The problem of scattering of neutral fermions in two-dimensional space-time is approached with a pseudoscalar potential step in the Dirac equation. Some unexpected aspects of the solutions beyond the absence of Klein\'{}s paradox are…

Using an effective strongly coupled lattice QCD Hamiltonian and Wilson fermions we calculate the equation of state for cold and dense quark matter by constructing an ansatz which exactly diagonalizes the Hamiltonian to second order in field…

We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term…

A supersymmetric analysis is presented for the d-dimensional Dirac equation with central potentials under spin-symmetric (S(r) = V(r)) and pseudo-spin-symmetric (S(r) = - V(r)) regimes. We construct the explicit shift operators that are…

The spherically symmetric potential $a \,\delta (r-r_0)+b\,\delta ' (r-r_0)$ is generalised for the $d$-dimensional space as a characterisation of a unique selfadjoint extension of the free Hamiltonian. For this extension of the Dirac…

We formulate an algebraic relativistic method of scattering for systems with spatially dependent mass based on the J-matrix method. The reference Hamiltonian is the three-dimensional Dirac Hamiltonian but with a mass that is…

Basically (2 + 1) dimensional Dirac equation with real deformed Lorentz scalar potential is investi gated in this study. The position dependent Fermi velocity function transforms Dirac Hamiltonian into a Klein-Gordon-like effective…