相关论文: Kepler problem in Dirac theory for a particle with…

A recursion technique of obtaining the asymptotical expansions for the bound-state energy eigenvalues of the radial Schr\"odinger equation with a position-dependent mass is presented. As an example of the application we calculate the energy…

This article studies the breaking of the Lorentz symmetry at the Planck length in quantum mechanics. We use three-dimensional p-adic vectors as position variables, while the time remains a real number. In this setting, the Planck length is…

One propose a relativistic version of the transfer matrix method for an electron moving through a given number of rectangular barriers of arbitrary shape. It is shown that starting with the Dirac equation depending on the effective mass and…

The kinetic energy operator with position-dependent-mass in plane polar coordinates is obtained. The separability of the corresponding Schr\"odinger equation is discussed. A hypothetical toy model is reported and two exactly solvable…

We study the three-dimensional Dirac and Klein-Gordon equations with scalar and vector potentials of equal magnitudes as an attempt to give a proper physical interpretation of this class of problems which has recently been accumulating…

We study the eigenvalues of the angular equation arising after the separation of the Dirac equation in the extreme Kerr metric. To this purpose a self-adjoint holomorphic operator family associated to this eigenvalue problem is considered.…

In this brief review, we survey the problem of electrostatic confinement of massless Dirac particles, via a number of exactly solvable one- and two-body models. By considering bound states at zero energy, we present a route to obtain truly…

We study the Dirac equation in a spacetime that represents the nonlinear superposition of the Schwarzchild solution to an external, stationary electromagnetic Berttoti-Robinson solution. We separate the Dirac equation into radial and…

We study the mathematical properties of a kinetic equation which describes the long time behaviour of solutions to the weak turbulence equation associated to the cubic nonlinear Schr\"odinger equation. In particular, we give a precise…

At zero energy the Dirac equation has interesting behaviour. The asymmetry in the number of spin up and spin down modes is determined by the topology of both space and the gauge field in which the system sits. An analogous phenomenon also…

We find the exact bound-state solutions and normalization constant for the Dirac equation with scalar-vector-pseudoscalar interaction terms for the generalized Hulth\'{e}n potential in the case where we have a particular mass function…

The paper analyzes time propagation of Dirac observables - using Heisenberg representation - in the light of various pseudodifferential operator algebras (cf. [Co3], [Co15], [Co16]). Our theory gives (i) a mechanical angular momentum (the…

A one-dimensional Schr\"odinger equation with position-dependent effective mass in the kinetic energy operator is studied in the framework of an $so(2,1)$ algebra. New mass-deformed versions of Scarf II, Morse and generalized…

Exact solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic…

We extend Panella and Roy's [13] work on one-dimensional heterostructure for massless Dirac particles with position-dependent (PD) velocity. We consider Dirac particles where both the mass and velocity are position-dependent. Bound states…

When a Dirac quantum state interacts with an applied electric field the energy of the quantum state changes. It is generally assumed that there is a maximum limit on the amount of energy that can be extracted from a Dirac quantum state, due…

Stabilizing, by deformation, the algebra of relativistic quantum mechanics a non-commutative space-time geometry is obtained. The exterior algebra of this geometry leads to an extended massless Dirac equation which has both a massless and a…

We consider the dynamic large deviation behaviour of Kac's collisional process for a range of initial conditions including equilibrium. We prove an upper bound with a rate function of the type which has previously been found for kinetic…

In his analysis of the Classical Theory of Radiating Electrons, Dirac (1938) draws attention to the characteristic instability of solutions to the third order equation of motion. He remarks that changing the sign of the self-force…

The Schr\"odinger-Pauli theory is generally believed to give a faithful representation of the nonrelativistic and weakly relativistic limit of the Dirac theory. However, the Schr\"odinger-Pauli theory is fundamentally incomplete in its…