Comment on ‘Energy profile of the one-dimensional Klein–Gordon oscillator’

2011 ◽  
Vol 84 (3) ◽  
pp. 037001 ◽  
Author(s):  
Abdelmalek Boumali ◽  
Abdelhakim Hafdallah ◽  
Amina Toumi
Keyword(s):  
Energy Profile ◽  
One Dimensional ◽  
Klein Gordon ◽  
The One

Energy profile of the one-dimensional Klein–Gordon oscillator

2007 ◽  
Vol 77 (1) ◽  
pp. 015003 ◽  
Author(s):  
Nagalakshmi A Rao ◽  
B A Kagali
Keyword(s):  
Energy Profile ◽  
One Dimensional ◽  
Klein Gordon ◽  
The One

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

scholarly journals Gap breathers in the one-dimensional Klein-Gordon diatomic chain

2007 ◽  
Vol 56 (2) ◽  
pp. 1041
Author(s):  
Li Mi-Shan ◽  
Tian Qiang
Keyword(s):  
One Dimensional ◽  
Diatomic Chain ◽  
Klein Gordon ◽  
The 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.

scholarly journals Superstatistics of the one-dimensional Klein-Gordon oscillator with energy-dependent potentials

2020 ◽  
Vol 66 (5 Sept-Oct) ◽  
pp. 671
Author(s):  
M. Labidi ◽  
A. Boumali ◽  
A. Ndem Ikot
Keyword(s):  
Thermal Properties ◽  
Partition Function ◽  
Thermodynamic Properties ◽  
Gamma Distribution ◽  
Low Energy ◽  
Tsallis Statistics ◽  
One Dimensional ◽  
Klein Gordon ◽  
The One ◽  
Energy Dependent

AbstractIn this paper, we investigated the influence of energy-dependent potentials on the thermodynamic properties of the Klein-Gordon oscillator(KGO): in this way all thermal properties have been determinate via the well-know Euler-Maclaurin method. After this, we extend our study to the case of superstatistical properties of our problem in question. The probability densityf(β)followsχ2− superstatistics (=Tsallis statistics or Gamma distribution). Under the approximation of the low-energy asymptotics of superstatistics, the partition function, at first, has been calculated. This approximation leads to a universal parameterqfor any superstatistics, not only for Tsallis statistics. By using the desired partition function, all thermal properties have been obtained in terms of the parameterq. Also, the influence of the this type of potentials on these properties, via the parameterγ, are well discussed.

Fast and High Accuracy Numerical Methods for the Solution of Nonlinear Klein–Gordon Equations

2011 ◽  
Vol 66 (12) ◽  
pp. 735-744 ◽  
Author(s):  
Akbar Mohebbi ◽  
Zohreh Asgari ◽  
Alimardan Shahrezaee
Keyword(s):  
Numerical Methods ◽  
High Efficiency ◽  
High Accuracy ◽  
Processing Unit ◽  
Conservation Of Energy ◽  
One Dimensional ◽  
Central Processing ◽  
Time Stepping ◽  
Klein Gordon ◽  
The One

In this work we propose fast and high accuracy numerical methods for the solution of the one dimensional nonlinear Klein-Gordon (KG) equations. These methods are based on applying fourth order time-stepping schemes in combination with discrete Fourier transform to numerically solve the KG equations. After transforming each equation to a system of ordinary differential equations, the linear operator is not diagonal, but we can implement the methods such as for the diagonal case which reduces the time in the central processing unit (CPU). In addition, the conservation of energy in KG equations is investigated. Numerical results obtained from solving several problems possessing periodic, single, and breather-soliton waves show the high efficiency and accuracy of the mentioned methods.

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