Related papers: Pekeris-type approximation for the $l$-wave in a P…
A new technique was recently developed to approximate the solution of the Schroedinger equation. This approximation (dubbed ERS) is shown to yield a better accuracy than the WKB-approximation. Here, we review the ERS approximation and its…
The trigonometric P\"oschl-Teller (PT) potential describes the diatomic molecular vibration. By using the Nikiforov-Uvarov (NU) method, we have obtained the exact analytical s-wave solutions of the radial Schr\"odinger equation (SE) for the…
Solutions of stationary Fokker-Planck equations in the narrow beam regime are commonly approximated by either ballistic linear transport or by a Fermi pencil-beam equation. We present a rigorous approximation analysis of these three models…
We show that solutions of the Schr\"odinger equation with a symmetric P\"oschl-Teller potential of a particular form can be expressed in terms of a closed combination (not series) of trigonometric functions. Using some properties of the…
Radial wave functions for power-law potentials are approximated with the help of power-law substitution and explicit summation of the leading constituent WKB series. Our approach reproduces the correct behavior of the wave functions at the…
The Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Poschl-Teller (tPT) potential including a Coulomb-like tensor interaction with arbitrary spin-orbit quantum number…
In this note, we give a probabilistic interpretation of the Central Limit Theorem used for approximating isotropic Gaussians in [1].
In this work, the analytical solution of the hyper-radial Schr\"{o}dinger equation for the spherical Woods-Saxon potential in D dimensions is presented. In our calculations, we have applied the Nikiforov-Uvarov method by using the Pekeris…
We show that one dimensional non-stationary Schr\"odi-nger equation with a specific choice of potential reduces to the quantum Painlev\'e II equation and the solution of its Riccati form appears as a dominant term of that potential.…
The radial part of Klein-Gordon equation is solved for the Woods-Saxon potential within the framework of an approximation to the centrifugal barrier. The bound states and the corresponding normalized eigenfunctions of the Woods-Saxon…
In this paper, an approximate solution to a specific class of the Fokker-Planck equation is proposed. The solution is based on the relationship between the Schr\"{o}dinger type equation with a partially confining and symmetrical potential.…
A general reformulation of classical sharp-edge diffraction theory is proposed within paraxial approximation. The, not so much known, Poincar\'e vector potential construction is employed directly inside Fresnel's 2D integral in order for it…
Considering fractional fast diffusion equations on bounded open polyhedral domains in $\mathbb{R}^N$, we give a fully Galerkin approximation of the solutions by $C^0$-piecewise linear finite elements in space and backward Euler…
It is shown that the Dunkl harmonic oscillator on the line can be generalized to a quasi-exactly solvable one, which is an anharmonic oscillator with $n+1$ known eigenstates for any $n\in \N$. It is also proved that the Hamiltonian of the…
We propose a new method to obtain approximate solutions for the Schr\"{o}dinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows in many cases to find analytical…
In this paper, we solve the D-dimensional Schr\"odinger equation with hyperbolic Poschl-Teller potential plus a generalized ring-shaped potential. After the separation of variable in the hyperspherical coordinate. We used Nikiforov-Uvarov…
An approximate method is proposed for the recovery of a compactly supported spherically-symmetric potential from the set of fixed-energy phase-shifts known for all angular momenta. The method reduces the inverse scattering problem to a…
The paper is devoted to the investigation of Esscher's transform on high dimensional Euclidean spaces in the light of its application to the central limit theorem. With this tool, we explore necessary and sufficient conditions of normal…
We apply the asymptotic iteration method (AIM) to obtain the solutions of Schrodinger equation in the presence of Poschl-Teller (PT) potential. We also obtain the solutions of Dirac equation for the same potential under the condition of…
For non-relativistic Schroedinger equations the lowering of their degree by substitution Psi(r) \to F(r) =Psi'(r) /Psi(r) is known to facilitate our understanding and use of their (incomplete, so called quasi-exact) solvability. We show…