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This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional…
An integral relation is established between the Green functions corresponding to two Hamiltonians which are supersymmetric (SUSY) partners and in general may possess both discrete and continuous spectra. It is shown that when the continuous…
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 study theoretically the level shift of the Dirac oscillator perturbed by any sharply peaked potential approaching a surface delta potential. A Green function method is used to obtain closed expressions for all partial waves and parities.
We define and study the properties of Darboux-type transformations between Sturm--Liouville problems with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter (including the Dirichlet boundary…
We study the unstable harmonic oscillator and the unstable linear potential in the presence of the point potential, which is the superposition of the Dirac $\delta(x)$ and the derivative $\delta'(x)$. Using the \textit{physical} boundary…
Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of…
We calculate the Green function for the Dirac equation describing a spin 1/2 particle in the presence of a potential which is a sum of the Coulomb potential V_C=-A_1/r and a Lorentz scalar potential V_S=-A_2/r. The bound state spectrum is…
We propose a general procedure to study double integrals arising when considering wave propagation in periodic structures. This method, based on a complex deformation of the integration surface to bypass the integrands' singularities, is…
A model in which a Dirac particle in $\mathbb{R}^{3}$ is bound by $N\geqslant1$ spatially distributed zero-range potentials is presented. Interactions between the particle and the potentials are modeled by subjecting a particle's bispinor…
We have proposed an analytical approach for exact solution of multi-channel scattering problems, in presence of Dirac Delta function couplings. Our solution is quite general and is valid for any set of potentials, if the Green's functions…
We study entire functions whose zeros and one-points lie on distinct finite systems of rays. General restrictions on these rays are obtained. Non-trivial examples of entire functions with zeros and one-points on different rays are…
The technique of differential intertwining operators (or Darboux transformation operators) is systematically applied to the one-dimensional Dirac equation. The following aspects are investigated: factorization of a polynomial of Dirac…
This work is devoted to the study of the existence and sign of Green's functions for first order linear problems with constant coefficients and initial (one point) conditions. We first prove a result on the existence of solutions of $n$-th…
The problem of a Dirac particle moving in a deformed Hulthen potential is solved in the framework of the path integral formalism. With the help of the Biedenharn transformation, the construction of a closed form for the Green's function of…
The connection between wave functions in the Dirac and Foldy-Wouthuysen representations is found. When the Foldy-Wouthuysen transformation is exact, upper spinors in two representations differ only by constant factors, and lower spinors in…
In this paper we will deduce several properties of the Green's functions related to the Hill's equation coupled to various boundary value conditions. In particular, the idea is to study the Green's functions of the second order differential…
In the present work we establish a simple relation between the Dirac equation with a scalar and an electromagnetic potentials in a two-dimensional case and a pair of decoupled Vekua equations. In general these Vekua equations are bicomplex.…
The rising interest in Dirac materials, condensed matter systems where low-energy electronic excitations are described by the relativistic Dirac Hamiltonian, entails a need for microscopic effective models to analytically describe their…
I provide a transfer matrix method for the Foldy-Wouthuysen representation of the Dirac equation. I derive the relationship between the reflection and transmission coefficients of the Dirac spinors and the wavefunction in the transformed…