相关论文: Exact solution of the 1D Dirac equation for the in…
An exact solution of the three-dimensional spherical symmetry inverse-square-root potential $V\left( r\right) =-\frac{\alpha}{\sqrt{r}}$, including scattering and bound-state solutions, is presented.
We present the exact solution of the stationary Schr\"odinger equation equation for the potential $V=V_0/{\sqrt{x}}$. Each of the two fundamental solutions that compose the general solution of the problem is given by a combination with…
We present a conditionally exactly solvable singular potential for the one-dimensional Schr\"odinger equation which involves the exactly solvable inverse square root potential. Each of the two fundamental solutions that compose the general…
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…
Utilizing an ${\it ansatz}$ for the eigenfunctions, we arrive at an exact closed form solution to the Schr\"{o}dinger equation with the inverse-power potential, $V(r)=ar^{-4}+br^{-3}+cr^{-2}+dr^{-1}$ in two dimensions, where the parameters…
In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of vector and scalar generalized Hartmann potentials. This is done provided the vector potential is equal to or minus the scalar…
We introduce an exactly integrable singular potential for which the solution of the one-dimensional stationary Schr\"odinger equation is written through irreducible linear combinations of the Gauss hypergeometric functions. The potential,…
We study the one-dimensional Dirac equation in the framework of a position dependent mass under the action of a Woods-Saxon external potential. We find that constraining appropriately the mass function it is possible to obtain a solution 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 obtain exact solutions of Dirac equation at zero kinetic energy for radial power-law relativistic potentials. It turns out that these are the relativistic extension of a subclass of exact solutions of Schrodinger equation with two-term…
We use a generalized scheme of supersymmetric quantum mechanics to obtain the energy spectrum and wave function for Dirac equation in (1+1)-dimensional spacetime coupled to a static scalar field.
We derive the node structure of the radial functions which are solutions of the Dirac equation with scalar $S$ and vector $V$ confining central potentials, in the conditions of exact spin or pseudospin symmetry, i.e., when one has $V=\pm…
The generalized Dirac oscillator as one of the exact solvable model in quantum mechanics was introduced in 2+1-dimensional world in this paper. What is more, the general expressions of the exact solutions for these models with the inverse…
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.
We present (exact) solutions of the Dirac equation with equally mixed interactions for a single fermion bounded by the family of fractional power singular potentials. Closed-form expressions as well as numerical values for the energies were…
The problem of a fermion subject to a general scalar potential in a two-dimensional world is mapped into a Sturm-Liouville problem for nonzero eigenenergies. The searching for possible bounded solutions is done in the circumstance of…
We study generalized (1+1)-dimensional Dirac oscillator in nonuniform electric field. It is shown that in the case of specially chosen electric field the eigenvalue equation can be casted in the form of supersymmetric quantum mechanics. It…
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…
We present the correct solution of the Dirac equation in 1+1 dimensions with the Lorentz scalar potential V(x)=g|x|.
We obtain the energy eigenvalues and radial wave functions of the D-Dimensional Dirac equation in the case of spin symmetry for Woods-Saxon potential in minimal length formalism. The radial part of the D-Dimensional Dirac equation is solved…