scholarly journals Scattering solutions of the Klein–Gordon equation for a step potential with hyperbolic tangent potential

2014 ◽  
Vol 29 (28) ◽  
pp. 1450146 ◽  
Author(s):  
Clara Rojas
Keyword(s):  
Reflection Coefficient ◽  
Transmission Coefficient ◽  
Hypergeometric Functions ◽  
Gordon Equation ◽  
Hyperbolic Tangent ◽  
Step Potential ◽  
Klein Gordon ◽  
Transmission Resonances ◽  
Klein Gordon Equation

We solve the Klein–Gordon equation for a step potential with hyperbolic tangent potential. The scattering solutions are derived in terms of hypergeometric functions. The reflection coefficient R and transmission coefficient T are calculated, we observed superradiance and transmission resonances.

scholarly journals Study of superradiance in the Lambert-W potential barrier

2019 ◽  
Vol 34 (16) ◽  
pp. 1950087 ◽  
Author(s):  
Luis Puente ◽  
Carlos Cocha ◽  
Clara Rojas
Keyword(s):  
Reflection Coefficient ◽  
Potential Barrier ◽  
Gordon Equation ◽  
Reflection Coefficients ◽  
Hyperbolic Tangent ◽  
Step Potential ◽  
Transmission And Reflection Coefficients ◽  
Klein Gordon ◽  
Klein Gordon Equation ◽  
Transmission And Reflection

We present a new potential barrier that presents the phenomenon of superradiance when the reflection coefficient [Formula: see text] is greater than one. We calculated the transmission and reflection coefficients for three different regions. The results are compared with those obtained for the hyperbolic tangent potential barrier and the step potential barrier. We also present the solution of the Klein–Gordon equation with the Lambert-[Formula: see text] potential barrier in terms of the Heun Confluent functions.

scholarly journals Scattering of a Klein–Gordon particle by a Hulthén potential

2009 ◽  
Vol 87 (9) ◽  
pp. 1021-1024 ◽  
Author(s):  
Jian-You Guo ◽  
Xiang-Zheng Fang
Keyword(s):  
Transmission Coefficient ◽  
Hypergeometric Functions ◽  
Gordon Equation ◽  
Wave Functions ◽  
Hulthén Potential ◽  
One Dimensional ◽  
Hulthen Potential ◽  
Klein Gordon ◽  
Transmission Resonances ◽  
Klein Gordon Equation

The Klein–Gordon equation in the presence of a spatially one-dimensional Hulthén potential is solved exactly and the scattering solutions are obtained in terms of hypergeometric functions. The transmission coefficient is derived by the matching conditions on the wave functions and the conditions for the existence of transmission resonances are investigated. It is shown how the zero-reflection condition depends on the shape of the potential.

scholarly journals Scattering of a scalar relativistic particle by the hyperbolic tangent potential

2015 ◽  
Vol 93 (1) ◽  
pp. 85-88 ◽  
Author(s):  
Clara Rojas
Keyword(s):  
Reflection Coefficient ◽  
Gamma Function ◽  
Hypergeometric Functions ◽  
Gordon Equation ◽  
Relativistic Particle ◽  
Hyperbolic Tangent ◽  
Klein Gordon ◽  
Klein Gordon Equation

We solve the Klein–Gordon equation in the presence of the hyperbolic tangent potential. The scattering solutions are derived in terms of hypergeometric functions. The reflection, R, and transmission, T, coefficients are calculated in terms of gamma function and, superradiance is discussed, when the reflection coefficient, R, is greater than one.

scholarly journals Scattering of a Klein–Gordon particle by a smooth barrier

2020 ◽  
Vol 98 (10) ◽  
pp. 939-943
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Potential Barrier ◽  
Gordon Equation ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Smoothness Parameter ◽  
Klein Gordon ◽  
Transmission Resonances ◽  
The One ◽  
Klein Gordon Equation

We present a study of the one-dimensional Klein–Gordon equation by a smooth barrier. The scattering solutions are given in terms of the Whittaker Mκ,μ(x) function. The reflection and transmission coefficients are calculated in terms of the energy, the height, and the smoothness of the potential barrier. For any value of the smoothness parameter we observed transmission resonances.

Pair creation in curved Snyder space

2020 ◽  
Vol 35 (04) ◽  
pp. 2050014 ◽  
Author(s):  
B. Hamil ◽  
M. Merad ◽  
T. Birkandan
Keyword(s):  
Electric Field ◽  
Hypergeometric Functions ◽  
Gordon Equation ◽  
Constant Electric Field ◽  
Pair Creation ◽  
Bogoliubov Transformation ◽  
Transformation Technique ◽  
Scalar Particles ◽  
Klein Gordon ◽  
Klein Gordon Equation

We study the problem of pair creation of scalar particles by an electric field in curved Snyder space. We find exact solutions for the Klein–Gordon equation with a constant electric field in terms of hypergeometric functions. Then we calculate the pair creation probability and the number of created pairs of particles through Bogoliubov transformation technique.

Schwinger mechanism on de Sitter background

2018 ◽  
Vol 33 (30) ◽  
pp. 1850177 ◽  
Author(s):  
B. Hamil ◽  
M. Merad
Keyword(s):  
Hypergeometric Functions ◽  
Gordon Equation ◽  
Constant Electric Field ◽  
Pair Creation ◽  
Bogoliubov Transformation ◽  
De Sitter ◽  
Klein Gordon ◽  
Sitter Background ◽  
Schwinger Mechanism ◽  
Klein Gordon Equation

In this paper, incorporating the effect of the deformed commutation relation on de Sitter background, we studied the deformed Schwinger mechanism in (1[Formula: see text]+[Formula: see text]1) dimensions for scalars particle of spin-0 in a constant electric field. The Klein–Gordon equation is solved exactly and the wave function is given in term of hypergeometric functions. The canonical method based on a Bogoliubov transformation is applied. The pair creation probability and the density number of created particles are calculated.

Approximate analytical solutions of scattering states for Klein-Gordon equation with Hulthén potentials for nonzero angular momentum

Open Physics ◽  
2008 ◽  
Vol 6 (4) ◽  
Author(s):  
Chang-Yuan Chen ◽  
Fa-Lin Lu ◽  
Dong-Sheng Sun
Keyword(s):  
Analytical Solutions ◽  
Hypergeometric Functions ◽  
Gordon Equation ◽  
Approximate Analytical Solution ◽  
Wave Functions ◽  
Calculation Formula ◽  
Scattering States ◽  
Approximate Analytical Solutions ◽  
Klein Gordon ◽  
Klein Gordon Equation

AbstractIn this paper, using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Klein-Gordon equation with the vector and scalar Hulthén potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of t-waves scattering states are presented. The normalized wave functions expressed in terms of hypergeometric functions of scattering states on the “k/2π scale” and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solution is discussed.

Solutions of the Coupled Klein-Gordon Equation by Modified Exp-Function Method

2011 ◽  
Vol 3 (3) ◽  
pp. 276-278
Author(s):  
Ram Dayal Pankaj ◽  
◽  
Arun Kumar
Keyword(s):  
Function Method ◽  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Fractional Klein-Gordon equation with singular mass

2021 ◽  
Vol 143 ◽  
pp. 110579
Author(s):  
Arshyn Altybay ◽  
Michael Ruzhansky ◽  
Mohammed Elamine Sebih ◽  
Niyaz Tokmagambetov
Keyword(s):  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation
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