相关论文: The Strong Levinson Theorem for the Dirac Equation
We consider several classes of symmetries of the Dirac Hamiltonian in 3+1 dimensions, with axially-deformed scalar and vector potentials. The symmetries include the known pseudospin and spin limits and additional symmetries which occur when…
Using the position as an independent variable, and time as the dependent variable, we derive the function ${\cal P}^{(\pm)}$, which generates the space evolution under the potential ${\cal V}(q)$ and Hamiltonian ${\cal H}$. Canonically…
We studied two possible approaches to one-dimensional Levinson's theorem for Sch\"odinger equation. The first one, we restrict the 3-dimensional theorem. The other one, the theorem proposed by Dong, Ma and Klauss \cite{Dong}. We find…
We deduce Levinson\'{}s theorem in non-relativistic quantum mechanics in one dimension as a sum rule for the spectral density constructed from asymptotic data. We assume a self-adjoint hamiltonian which guarantees completeness; the…
We introduce a Dirac equation which reproduces the usual radial sextic oscillator potential in the non-relativistic limit. We determine its energy spectrum in the presence of the magnetic field. It is shown that the equation is solved in…
Consider a semiclassical Hamiltonian $H := h^{2} \Delta + V - E$ where $\Delta$ is the positive Laplacian on $\mathbb{R}^{d}$, $V \in C^{\infty}_{0}(\mathbb{R}^{d})$ and $E > 0$ is an energy level. We prove that under an appropriate…
We study vacuum polarization due to strong fields, in the presence of an electron-positron plasma. For this purpose, we expand quantum kinetic equations using weak fields and slow temporal scales as expansion parameters. It is demonstrated…
The formalism of two coupled Dirac equations within constraint instant form dynamics is used to study the nucleon-nucleon interaction. The salient features and the final Schroedinger type equation is given. Explicitly energy dependent…
An approximate solution of the position-dependent mass Dirac equation with the Hulthen potential is obtained in $D$-dimensions within frame work of an exponential approximation of the centrifugal term. The relativistic energy spectrum is…
The Dirac equation is one of the most fundamental equations of modern physics. It is a spinor equation, but some tensor equivalents of the equation were proposed previously. Those equivalents were either nonlinear or involved several…
The well known Klein paradox for the relativistic Dirac wave equation consists in the computation of possible ``negative probabilities'' induced by certain potentials in some regimes of energy. The paradox may be resolved employing the…
The well known Klein paradox for the relativistic Dirac wave equation consists in the computation of possible ``negative probabilities'' induced by certain potentials in some regimes of energy. The paradox may be resolved employing the…
The relativistic problem of fermions subject to a PT-symmetric potential in the presence of position-dependent mass is reinvestigated. The influence of the PT-symmetric potential in the continuity equation and in the orthonormalization…
We study the behavior of persistent current of relativistic electrons on a one dimensional ring in presence of attractive/repulsive scattering potentials. In particular, we investigate the persistent current in accordance with the strength…
We obtain exact solution of the Dirac equation for a charged particle with position-dependent mass in the Coulomb field. The effective mass of the spinor has a relativistic component which is proportional to the square of the Compton…
A single Dirac particle is bound in d dimensions by vector V(r) and scalar S(r) central potentials. The spin-symmetric S=V and pseudo-spin-symmetric S = - V cases are studied and it is shown that if two such potentials are ordered V^{(1)}…
We study the energy critical wave equation in 3 dimensions around a single soliton. We obtain energy boundedness (modulo unstable modes) for the linearised problem. We use this to construct scattering solutions in a neighbourhood of…
The field equation for a spin 1/2 massive charged particle propagating in spacetimes that are the direct product of 2-dimensional spaces is separated. Moreover, we use this result to attain the separability of the Dirac equation in some…
It is shown that in the two-dimensional space-time the dynamic system, described by the free Klein-Gordon equation, turns to the dynamic system, described by the free Dirac equation, provided the current and the energy-momentum tensor are…
It is argued from geometrical, group-theoretical and physical points of view that in the framework of QCD it is not only necessary but also possible to modify the Dirac equation so that correspondence principle holds valid. The Dirac wave…