Related papers: Instantaneous Reflection and Transmission Coeffici…
In this paper, we calculate the transmission and reflection amplitudes of wave functions for different potentials such as the delta function, the rectangular barrier, the Eckart potential, and the Hulthen potential. We describe the…
We derive an expression for the conditional time for the reflection of a wave from an arbitrary potential barrier using the WKB wavefunction in the barrier region. Our result indicates that the conditional times for transmission and…
We discuss the method of calculating the reflection coefficient using complex trajectory WKB (CWKB) approximation. This enables us to give an interpretation of non-reflecting nature of the potential under certain conditions and clarify some…
The reflection and transmission of wave functions at a potential step is a well-known issue in a textbook of quantum mechanics. We studied the reflection and transmission characteristics analytically when the potential step is moving at a…
The paper presents the results of a study of the possibility of using the WKB approach to describe Inhomogeneous Travelling-Wave Accelerating Sections (ITWAS). This possibility not only simplifies the calculation, but also allows the use of…
Methods for calculating the transmission coefficient are proposed, all of which arise from improved non-reflecting WKB boundary conditions at the edge of the computational domain in 1-dimensional geometries. In the first, the…
We present a new methodology, based on the WKB approximation and Fast Fourier Transforms, for the evaluation of wave propagation through inhomogeneous media. This method can accurately resolve fields containing caustics, while still…
Reliable control of the deposition process of optical films and coatings frequently requires monitoring of the refractive index profile throughout the layer. In the present work a simple in situ approach is proposed which uses a WKBJ matrix…
In this paper we revisit the one-dimensional tunneling problem. We consider Kemble's approximation for the transmission coefficient. We show how this approximation can be extended to above-barrier energies by performing the analytical…
The scattering properties of quantum particles on fractal potentials at different stages of fractal growth are obtained by means of the transfer matrix method. This approach can be easily adopted for project assignments in introductory…
Eikonal, or ray tracing, methods are commonly used to estimate the propagation of radio frequency fields in plasmas. While the information gained from the rays is quite useful, an approximate solution for the fields would also be valuable,…
This paper shows that WKB wave function can be expressed in the form of an adiabatic expansion. To build a bridge between two widely invoked approximation schemes seems pedagogically instructive. Further "cubic-WKB" method that has been…
In this work we present the results of calculation of the electric field distribution in the inhomogeneous media based on the generalized WKB method. In this approach the field is represented as the sum of two components, one of which is…
Some commonly used approximations for complete fusion and breakup transmission coefficients in collisions of weakly bound projectiles at near barrier energies are assessed. We show that they strongly depend on the adopted classical…
A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an…
The Differential Transfer Matrix Method is extended to the complex plane, which allows dealing with singularities at turning points. The result for real-valued systems are simplified and a pair of basis functions is found. These bases are a…
On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a…
A method, recently devised to obtain analytical approximations to certain classes of integrals, is used in combination with the WKB expansion to derive accurate analytical expressions for the spectrum of quantum potentials. The accuracy of…
We study transmission and reflection properties of a perfectly amplifying as well as absorbing medium analytically by using the tight binding equation. Different expressions for transmittance and reflectance are obtained for even and odd…
A general algorithm for calculating the reflection and refraction of nonuniform plane waves from an arbitrarily oriented and charged planar interface between two lossy isotropic media is proposed based on the decomposition of the complex…