Related papers: On Conformal d'Alembert-Like Equations
In this paper we utilize the covariance of Ricatti equation with respect to linear fractional transformations to define classes of conformally equivalent second order differential equations. This motivates then the introduction of…
We study the three-dimensional Dirac and Klein-Gordon equations with scalar and vector potentials of equal magnitudes as an attempt to give a proper physical interpretation of this class of problems which has recently been accumulating…
In this work, we extend the time-dependent conformable Schr\"odinger equation for a fractional dimensional system of N spatial coordinates to be used as an effective description of anisotropic and confined systems. A specific example is…
Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second order differential equation. Differential equations of this standard form are solvable in terms…
In two recent papers, an isometric conformal transformation has been introduced that eliminates potential interaction terms from the Schr\"odinger equation for central potential problems. The method has been demonstrated for both the…
One dimensional Klein-Gordon (KG) equation is investigated in the domain of conformable fractional calculus for one dimensional scalar potential namely generalized Hulthen potential. The conformable fractional calculus is based on…
We prove that a compactly supported perturbation of a rational or simply periodic algebro-geometric potential of the one-dimensional Schr\"odinger equation on the half line is uniquely determined by the location of its Dirichlet eigenvalues…
We propose a natural family of higher-order partial differential equations generalizing the second-order Klein-Gordon equation. We characterize the associated model by means of a generalized action for a scalar field, containing…
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…
The Calder\'on problem for the fractional Schr\"odinger equation was introduced in the work \cite{GSU}, which gave a global uniqueness result also in the partial data case. This article improves this result in two ways. First, we prove a…
Recent studies show that deformations in quantum mechanics are inevitable. In this contribution, we consider a relativistic quantum mechanical differential equation in the presence of Dunkl operator-based deformation and we investigate…
In a recent paper, it has been shown the Schr\"{o}dinger equation for the three-dimensional harmonic oscillator can be simplified through the use of an isometric conformal transformation. Here, it is demonstrated that the same…
In this study, linear second-order conformable differential equations using a proportional derivative are shown to be formally self-adjoint equations with respect to a certain inner product and the associated self-adjoint boundary…
It is shown that the radial Schroedinger equation for a power law potential and a particular angular momentum may be transformed using a change of variable into another Schroedinger equation for a different power law potential and a…
We introduce the Dunkl--Klein--Gordon (DKG) equation in 2D by changing the standard partial derivatives by the Dunkl derivatives in the standard Klein--Gordon (KG) equation. We show that the generalization with Dunkl derivative of the…
Approximate analytical solutions of a two-term potential are studied for the relativistic wave equations, namely, for the Klein-Gordon and Dirac equations. The results are obtained by solving of a Riemann-type equation whose solution can be…
We use the Klein-Gordon equation in a curved spacetime to construct the relativistic analog of the Schr\"odinger-Newton problem, where a scalar particle lives in a gravitational potential well generated by its own probability distribution.…
We present, for the first time, exact solutions for the Schr\"{o}dinger equation in Moon and Spencer's toroidal coordinates, and in the electromagnetic toroidal--poloidal coordinate systems. Curiously, both systems present a fractional…
The historical Klein-Gordon transformation of complex-valued first-order in time Schroedinger equations iterates these in a naively straightforward way which changes them into complex-valued second-order in time equations that have a…
A new discretization of the radial equations that appear in the solution of separable second order partial differential equations with some rotational symmetry (as the Schrodinger equation in a central potential) is presented. It cures a…