相关论文: The Extended Wronskian Determinant Approach and th…

A Wronskian determinant approach is suggested to study the energy and the wave function for one-dimensional Schrodinger equation. An integral equation and the corresponding Green's function are constructed. As an example, we employed this…

We consider a single particle which is bound by a central potential and obeys the Dirac equation in d dimensions. We first apply the asymptotic iteration method to recover the known exact solutions for the pure Coulomb case. For a…

The extended Cornell potential which the harmonic oscillator potential is included in the original Cornell potential. The Dirac equation is solved by reducing the Dirac equation to the form of Schrodinger equation. The Nikiforov-Uvarov…

The aim of this work is to find exact solutions of the one-dimensional Dirac equation that do not belong to the already known conventional class. We write the spinor wavefunction as a bounded infinite sum in a complete basis set, which is…

An analytical solution of the Dirac equation with a Cornell potential, with identical scalar and vectorial parts, is presented. The solution is obtained by using the linear potential solution, related to Airy functions, multiplied by…

We present the first exact calculation of the energy of the bound state of a one dimensional Dirac massive particle in weak short-range arbitrary potentials, using perturbation theory to fourth order (the analogous result for two…

This paper aims at extending our previous work on the solution of the one-dimensional Dirac equation using the Tridiagonal Representation Approach (TRA). In the approach, we expand the spinor wavefunction in terms of suitable square…

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…

The Dirac equation for H$_2^+$ is solved numerically using an iterative method proposed by Kutzelnigg [Z. Phys. 11, 15 (1989]. The four-component wavefunction is expanded in a newly introduced kinetically balanced exponential basis set. The…

We solve the one-dimensional Dirac equation by taking into account the possibility of position-dependence in the mass function. We also take the Fermi velocity to act as a local variable and examine the combined effects of the two on the…

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…

By using two-component approach to the one-dimensional effective mass Dirac equation bound states are investigated under the effect of two new non-PT-symmetric, and non-Hermitian, exponential type potentials. It is observed that the Dirac…

A method for approximate solution of initial value and spectral problems for one dimensional Dirac equation based on an analytic approximation of the transmutation operator is presented. In fact the problem of numerical approximation of…

We solve the Dirac equation in one space dimension for the case of a linear, Lorentz-scalar potential. This extends earlier work of Bhalerao and Ram [Am. J. Phys. 69 (7), 817-818 (2001)] by eliminating unnecessary constraints. The spectrum…

We propose a simple and straightforward method based on Wronskians for the calculation of bound--state energies and wavefunctions of one--dimensional quantum--mechanical problems. We explicitly discuss the asymptotic behavior of the…

The Fermi acceleration mechanism is a significant source of cosmic rays. When the width of a potential well changes over time, the velocity of particles within the well also changes. For quantum systems, such dynamics should be described by…

Exact analytic 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…

The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong…

Exact solution of the Dirac equation for a special form of the Woods-Saxon potential is obtained for the s-states. The energy eigenvalues and two-component spinor wave functions are derived by using a systematical method which is called as…

We solve the general one-dimensional Dirac equation using a "Poincare Map" approach which avoids any approximation to the spacial derivatives and reduces the problem to a simple recursive relation which is very practical from the numerical…