Related papers: The Dirac-Coulomb Problem: a mathematical revisit
Integrable models of resonant interaction of two or more waves in 1+1 dimensions are known to be of applicative interest in several areas. Here we consider a system of three coupled wave equations which includes as special cases the vector…
Darboux developed an ingenious algebraic mechanism to construct infinite chains of ''integrable'' second-order differential equations as well as their solutions. After a surprisingly long time, Darboux's results were rediscovered and…
In this paper, we study the theory of orthogonal trigonometric polynomials (OTP). We obtain asymptotics of OTP with positive and analytic weight functions by Riemann-Hilbert approach and find they have relations with orthogonal polynomials…
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…
The Dirac equation is used to provide a relativistic calculation of the binding energy of a hydrogen-like atom confined within a penetrable spherical barrier. We take the potential to be Coulombic within the barrier and constant outside the…
A method for solving an inverse spectral problem for the one-dimensional Dirac equation is developed. The method is based on the Gelfand-Levitan equation and the Fourier-Legendre series expansion of the transmutation kernel. A linear…
Using the approach the modified Euler-Lagrange field equation together with the corresponding Seiberg-Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. We then find the noncommutative…
Radiative corrections which remove accidental degeneracy in the spectrum of the relativistic hydrogen atom and lead to the modification of the Coulomb law, are calculated within the novel approach, based on the exact solution of the Dirac…
The series solution of the radial part of the Schr\"odinger equation for simultaneous coulomb and harmonic potential involves three-term recursion relation and is thus difficult to solve for bound states. We have suggested a simple method…
The discrete non-commutative Darboux system of equations with self-consistent sources is constructed, utilizing both the vectorial fundamental (binary Darboux) transformation and the method of additional independent variables. Then the…
Approximate analytical solutions of the Dirac equation are obtained for some diatomic molecular potentials plus a tensor interaction with spin and pseudospin symmetries with any angular momentum. We find the energy eigenvalue equations in…
The closed form integral representation for the projection onto the subspace spanned by bound states of the two-body Coulomb Hamiltonian is obtained. The projection operator onto the $n^2$ dimensional subspace corresponding to the $n$-th…
We analyze the parabolic Dirac operator $D \pm i\partial_t$ in a biquaternionic setting, characterizing its kernel via generalized div-curl systems and Cauchy-Riemann-type relations between the real and imaginary parts. Using the machinery…
We obtain the two-point Green's function for the relativistic Dirac-Oscillator problem. This is accomplished by setting up the relativistic problem in such a way that makes comparison with the nonrelativistic problem highly transparent and…
This is the second article in which we study the rotating Morse potential model for diatomic molecules using the tridiagonal J-matrix approach. Here, we improve further the accuracy of computing the bound states and resonance energies for…
Using the operator representation of the Dirac Coulomb Green function the analytical method in perturbation theory is employed in obtaining solutions of the Dirac equation for a hydrogen-like atom in a time-dependent electric field. The…
A procedure to recover explicitly self-adjoint matrix Dirac systems on semi-axis (with both discrete and continuous components of spectrum) from rational Weyl functions is considered. Its stability is proved. GBDT version of…
We examine the bound state solutions of the Dirac equation under the spin and pseudospin symmetries for a new suggested combined potential, Hulten plus a class of Yukawa potential including a Coulomb-like tensor interaction. An improved…
We develop analytical methods for nonlinear Dirac equations. Examples of such equations include Dirac-harmonic maps with curvature term and the equations describing the generalized Weierstrass representation of surfaces in three-manifolds.…
We study the Dirac equation in 3+1 dimensions with non-minimal coupling to isotropic radial three-vector potential and in the presence of static electromagnetic potential. The space component of the electromagnetic potential has angular…