Related papers: Solution of the relativistic Dirac-Hulthen problem
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…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support a tridiagonal matrix representation of the wave operator. Doing so results in exactly solvable problems with a…
We present a systematic approach for the separation of variables for the two-dimensional Dirac equation in polar coordinates. The three vector potential, which couple to the Dirac spinor via minimal coupling, along with the scalar potential…
A first-order relativistic wave equation is constructed in five dimensions. Its solutions are eight-component spinors, which are interpreted as single-particle fermion wave functions in four-dimensional spacetime. Use of a ``cylinder…
Dirac equation is solved for some exponential potentials, hypergeometric-type potential, generalized Morse potential and Poschl-Teller potential with any spin-orbit quantum number $\kappa$ in the case of spin and pseudospin symmetry,…
A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar $S$ and a vector $V$ quadratic potentials in the radial coordinate, as well as a tensor potential $U$ linear in $r$.…
The Dirac Hamiltonian with relativistic scalar and vector harmonic oscillator potentials has been solved analytically in two limits. One is the spin limit for which spin is an invariant symmetry of the the Dirac Hamiltonian and the other is…
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…
In some quantum chemical applications, the potential models are linear combination of single exactly solvable potentials. This is the case equivalent of the Stark effect for a charged harmonic oscillator (HO) in a uniform electric field of…
An elementary treatment of the Dirac Equation in the presence of a three-dimensional spherically symmetric $\delta (r-r_0)$-potential is presented. We show how to handle the matching conditions in the configuration space, and discuss the…
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…
We introduce the new, exactly solvable model of the two-dimensional Dirac fermion in presence of an asymmetric, P\"oschl-Teller-like vector potential. Utilizing the translation invariance of the system, the effective one-dimensional…
In this {\bf draft version} we prove inhomogeneous Strichartz estimates with spherical symmetry in the abstract setting via duality arguments. Then we derive some new explicit estimates in the context of the wave equation. This allows us to…
We present the exact analytical solution of the radial Schr\"{o}dinger equation for the deformed Hulth\'{e}n and the Morse potentials within the framework of the Asymptotic Iteration Method. The bound state energy eigenvalues and…
A non-perturbative approach to the solution of the time-dependent, two-center Dirac equation is presented with a special emphasis on the proper treatment of the potential of the nuclei. In order to account for the full multipole expansion…
An approximate solution of the Schrodinger equation with the Hulth$\acute{e}$n potential is obtained in D-dimensions with an exponential approximation of the centrifugal term. Solution to the corresponding hyper-radial equation is given…
In the present article we have found the complete energy spectrum and the corresponding eigenfunctions of the Dirac oscillator in two spatial dimensions. We show that the energy spectrum depends on the spin of the Dirac particle.
We obtain classes of two dimensional static Lorentzian manifolds, which through the supersymmetric formalism of quantum mechanics admit the exact solvability of Dirac equation on these curved backgrounds. Specially in the case of a modified…
In this article, we present the analytical solution of the radial Schr\"{o}dinger equation for the Hulth\'{e}n potential within the framework of the asymptotic iteration method by using an approximation to the centrifugal potential for any…
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…