Related papers: Delta potentials revisited via Fourier transform
We present the framework of delta-complete analysis for bounded reachability problems of general hybrid systems. We perform bounded reachability checking through solving delta-decision problems over the reals. The techniques take into…
Renormalization is one of the deepest ideas in physics, yet its exact implementation in any interesting problem is usually very hard. In the present work, following the approach by Glazek and Maslowski in the flat space, we will study the…
The problem of a spin-free electron with mass $m$, charge $e$ confined onto a ring of radius $R_0$ and with an attractive Dirac delta potential with scaling factor (depth) $\kappa$ in non-relativistic theory has closed form analytical…
We obtain three new solvable, real, shape invariant potentials starting from the harmonic oscillator, P\"oschl-Teller I and P\"oschl-Teller II potentials on the half-axis and extending their domain to the full line, while taking special…
In two and three dimensions, the standard treatment of the scattering problem for a multi-delta-function potential, $v(\mathbf{r})=\sum_{n=1}^N\mathfrak{z}_n\delta(\mathbf{r}-\mathbf{a}_n)$, leads to divergent terms. Regularization of these…
We propose a simpler derivation of the probability density function of Feller Diffusion using the Fourier Transform and solving the resulting equation via the Method of Characteristics. We also discuss simulation algorithms and confirm key…
Approximate bound state solutions of the spinless Salpeter equation for the Hellmann potential are studied for heavy particles. By using functional analysis method, an analytical expression for the energy levels, and the corresponding…
In this work, we present a phenomenological study of the complete analytical solution to the bound eigenstates and eigenvalues of the Yukawa potential obtained previously using the hidden supersymmetry of the system and a systematic…
This work presents results on solutions of the one-dimensional damped wave equation, also called telegrapher's equation, when the initial conditions are general distributions, not only functions. We make a complete deduction of its…
A generalized definition of superpotential has proposed, which connects two one-dimensional potentials $V_{1}$ and $V_{2}$ with discrete energy spectra completely and where: 1) energy of factorization equals to arbitrary level of spectrum…
We address two questions regarding square-well potentials from a didactic perspective. The first question concerns whether or not the justification of the standard a priori omission of the potential's vertical segments in the analysis of…
By careful exploration of separation of variables into the Laplacian in spherical coordinates, we obtain the extra delta-like singularity, elimination of which restricts the radial wave function at the origin. This constraint has the form…
We investigate the existence and the singular structure of delta wave solutions to a semilinear strictly hyperbolic equation with strongly singular initial and boundary conditions. The boundary conditions are given in nonlocal form with a…
We consider a single particle which is bound by a central potential and obeys the Dirac equation in d dimensions. We first apply the asymptotic iteration method to recover the known exact solutions for the pure Coulomb case. For a…
We discuss electron scattering in a one-dimensional delta barrier potential with either time-dependent coupling constant (classical model) or a coupling constant that is linear in a boson coordinate (quantum model). We find an exact…
Tunneling of electrons through a barrier with complex potential is investigated. We focus on two cases, symmetric double rectangular barrier and double delta potential barrier, and give expressions for resonant transmission probability for…
We propose a new method to construct a four parameter family of quantum-mechanical point interactions in one dimension, which is known as all possible self-adjoint extensions of the symmetric operator $T=-\Delta \lceil C^{\infty}_{0}({\bf…
It is known that the unified transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coefficient evolution equation on the finite interval or the half-line. In contrast, classical methods…
Potentials play an important role in solving boundary value problems for elliptic equations. In the middle of the last century, a potential theory was constructed for a two-dimensional elliptic equation with one singular coefficient. In the…
The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods-Saxon potential reported in [Phys. Rev. C 72, 027001 (2005)] is extended to the fractional forms using the generalized fractional derivative…