scholarly journals Scattering State of Klein-Gordon Particles by q-Parameter Hyperbolic Poschl-Teller Potential

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Akpan Ndem Ikot ◽  
Hillary P. Obong ◽  
Israel O. Owate ◽  
Michael C. Onyeaju ◽  
Hassan Hassanabadi
Keyword(s):  
Bound States ◽  
Hypergeometric Functions ◽  
Energy Equation ◽  
Bound State ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Scattering State ◽  
Klein Gordon ◽  
The One

The one-dimensional Klein-Gordon equation for equal vector and scalar q-parameter hyperbolic Poschl-Teller potential is solved in terms of the hypergeometric functions. We calculate in detail the solutions of the scattering and bound states. By virtue of the conditions of equation of continuity of the wave functions, we obtained explicit expressions for the reflection and transmission coefficients and energy equation for the bound state solutions.

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 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 BOUND STATES OF THE KLEIN–GORDON EQUATION IN THE PRESENCE OF SHORT RANGE POTENTIALS

2006 ◽  
Vol 21 (02) ◽  
pp. 313-325 ◽  
Author(s):  
VÍCTOR M. VILLALBA ◽  
CLARA ROJAS
Keyword(s):  
Short Range ◽  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
One Dimensional ◽  
Klein Gordon ◽  
Klein Gordon Equation

We solve the Klein–Gordon equation in the presence of a spatially one-dimensional cusp potential. The bound state solutions are derived and the antiparticle bound state is discussed.

scholarly journals Generalized relativistic wave equations with intrinsic maximum momentum

2014 ◽  
Vol 29 (15) ◽  
pp. 1450080 ◽  
Author(s):  
Chee Leong Ching ◽  
Wei Khim Ng
Keyword(s):  
Bound States ◽  
Wave Equations ◽  
Scalar Potential ◽  
Bound State ◽  
Relativistic Wave Equations ◽  
Wave Functions ◽  
Relativistic Wave ◽  
One Dimensional ◽  
Nonperturbative Effect ◽  
Klein Gordon

We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wave functions of one-dimensional Klein–Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential is stronger than vector potential. The energy spectrum of the systems studied is bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.

Transmission resonance for a Dirac particle in a one-dimensional Hulthén potential

Open Physics ◽  
2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Jianyou Guo ◽  
Yi Yu ◽  
Shaowei Jin
Keyword(s):  
Hypergeometric Functions ◽  
Matching Condition ◽  
Dirac Particle ◽  
Hulthén Potential ◽  
Transmission Resonance ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Hulthen Potential ◽  
Scattering States

AbstractWe have solved exactly the two-component Dirac equation in the presence of a spatially one-dimensional Hulthén potential, and presented the Dirac spinors of scattering states in terms of hypergeometric functions. We have derived the reflection and transmission coefficients using the matching condition on the wavefunctions, and investigated the condition for the existence of transmission resonance. Furthermore, we have demonstrated how the transmission resonance depends on the shape of the potential.

EXACT SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE ROSEN–MORSE TYPE POTENTIALS VIA NIKIFOROV–UVAROV METHOD

2008 ◽  
Vol 23 (35) ◽  
pp. 3005-3013 ◽  
Author(s):  
A. REZAEI AKBARIEH ◽  
H. MOTAVALI
Keyword(s):  
Exact Solutions ◽  
Gordon Equation ◽  
Bound State ◽  
S Wave ◽  
Vector Potentials ◽  
Klein Gordon ◽  
The One ◽  
Uvarov Method ◽  
Equal Scalar ◽  
Klein Gordon Equation

The exact solutions of the one-dimensional Klein–Gordon equation for the Rosen–Morse type potential with equal scalar and vector potentials are presented. First, we briefly review Nikiforov–Uvarov mathematical method. Using this method, wave functions and corresponding exact energy equation are obtained for the s-wave bound state. It has been shown that the results for Rosen–Morse type potentials reduce to the standard Rosen–Morse well and Eckart potentials in the special case. The PT-symmetry for these potentials is also considered.

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 Instability of charged massive scalar fields in bound states around Kerr–Sen black holes

2015 ◽  
Vol 24 (14) ◽  
pp. 1550102 ◽  
Author(s):  
Haryanto M. Siahaan
Keyword(s):  
Black Holes ◽  
Bound States ◽  
Gordon Equation ◽  
Scalar Fields ◽  
Bound State ◽  
Imaginary Component ◽  
Scalar Perturbation ◽  
Massive Scalar ◽  
Massive Scalar Field ◽  
Klein Gordon

In this paper, we show the instability of a charged massive scalar field in bound states around Kerr–Sen black holes. By matching the near and far region solutions of the radial part in the corresponding Klein–Gordon equation, one can show that the frequency of bound state scalar fields contains an imaginary component which gives rise to an amplification factor for the fields. Hence, the unstable modes for a charged and massive scalar perturbation in Kerr–Sen background can be shown.

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
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