Related papers: Laplace equation for the Dirac, Euler and the harm…
We apply the Dirac factorization method to the nonrelativistic harmonic oscillator and, more in general, to Hamiltonians with a generic potential. It is shown that this procedure naturally leads to a supersymmetric formulation of the…
We find solutions of Laplace's equation with specific boundary conditions (in which such solutions take either the value zero or unity in each surface) using a generic curvilinear system of coordinates. Such purely geometrical solutions…
We give the solution of certain parabolic evolution problems (time-depending perturbations of the heat equation for the harmonic oscillator) as explicit integrals on the Wiener space.
In this paper, we study the Dirichlet problem for Laplace's equation in an open disk. The uniqueness of solutions is ensured by the well-known weak maximum principle. We introduce a novel approach to demonstrate the existence of a solution…
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.…
In this paper, we give a correct definition of the Laplace operator with delta-like potentials. Correctly solvable pointwise perturbation is investigated and formulas of resolvent are described. We study some properties of the resolvent. In…
We discuss the Dirac oscillator in $(1+1)$ and $(2+1)$ dimensions and generalize it in the spirit of the isotonic oscillator using supersymmetric quantum mechanics. In $(1+1)$ dimensions, the Dirac oscillator returns to the quantum harmonic…
We consider the Dirac equations in static spherically-symmetric space-times, and we present a type of spinor field whose structure allows the separation of elevation angle and radial coordinate in very general situations. We demonstrate…
In this paper we study the (2 + 1)-dimensional Dirac oscillator in the noncommutative phase space and the energy eigenvalues and the corresponding wave functions of the system are obtained through the sl(2) algebraization. It is shown that…
In this work we study and exactly solve the Dirac oscillator with three different topological defects, namely the cosmic string spacetime ($\Lambda_\mp$), the magnetic cosmic string spacetime ($\Theta_\mp$) and the cosmic dislocation…
Classical oscillator differential equation is replaced by the corresponding (finite time) difference equation. The equation is, then, symmetrized so that it remains invariant under the change d going to -d, where d is the smallest span of…
The complete energy spectrum for the Dirac oscillator via R-deformed Heisenberg algebra is investigated.
We demonstrate that neutral Dirac particles in external electric fields, which are equivalent to generalized Dirac oscillators, are physical examples of quasi-exactly solvable systems. Electric field configurations permitting quasi-exact…
The Ermakov equation, appearing in quantum mechanics of a harmonic oscillator, is extended via dissipative and thermal terms to take into account the effect of an environment.
In this work we consider the Neumann problem for the Laplace operator and we prove an existence result in the H\"older spaces and obtain Schauder estimates. According to our knowledge this result is not explicitly proved in the several…
The oscillator-like interaction is introduced in the equation for the particle of arbitrary spin, given by Dirac and re-written to a matrix form by Dowker.
We study the semirelativistic Hamiltonian operator composed of the relativistic kinetic energy and a static harmonic-oscillator potential in three spatial dimensions and construct, for bound states with vanishing orbital angular momentum,…
The Schr\"{o}dinger equation and ladder operators for the harmonic oscillator are shown to simplify through the use of an isometric conformal transformation. These results are discussed in relation to the Bargmann representation. It is…
In this paper, under some integrability condition, we prove that an electrical perturbation of the discrete Dirac operator has purely absolutely continuous spectrum for the one dimensional case. We reduce the problem to a non-self-adjoint…
We obtain exact solution of the Dirac equation with the Coulomb potential as an infinite series of square integrable functions. This solution is for all energies, the discrete as well as the continuous. The spinor basis elements are written…