The Klein–Gordon equation with the Kratzer potential in the noncommutative space

2018 ◽  
Vol 33 (35) ◽  
pp. 1850203 ◽  
Author(s):  
M. Darroodi ◽  
H. Mehraban ◽  
S. Hassanabadi
Keyword(s):  
Perturbation Theory ◽  
Phase Space ◽  
Gordon Equation ◽  
Energy Shift ◽  
Laboratory Frame ◽  
Noncommutative Space ◽  
Noncommutative Phase Space ◽  
Polar Coordinate ◽  
Klein Gordon ◽  
Klein Gordon Equation

The Klein–Gordon equation is considered for the Kratzer potential in the spherical polar coordinate in laboratory frame in noncommutative space. The energy shift due to noncommutativity is obtained via the perturbation theory. After rather cumbersome algebra, we found the eigenfunctions and eigenvalues of the system for a noncommutative phase space.

scholarly journals KLEIN–GORDON EQUATION FOR THE COULOMB POTENTIAL IN NONCOMMUTATIVE SPACE

2010 ◽  
Vol 25 (29) ◽  
pp. 2523-2528 ◽  
Author(s):  
HOSSEIN MOTAVALLI ◽  
AMIN REZAEI AKBARIEH
Keyword(s):  
Perturbation Theory ◽  
Spectral Line ◽  
Coulomb Potential ◽  
Gordon Equation ◽  
Energy Shift ◽  
Noncommutative Space ◽  
Commutative Space ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this paper the stationary Klein–Gordon equation is considered for the Coulomb potential in noncommutative space. The energy shift due to noncommutativity is obtained via the perturbation theory. Furthermore, we show that the degeneracy of the initial spectral line is broken in transition from commutative space to noncommutative space.

scholarly journals LOGARITHMIC PERTURBATION THEORY FOR RADIAL KLEIN–GORDON EQUATION WITH SCREENED COULOMB POTENTIALS VIA ℏ-EXPANSIONS

2004 ◽  
Vol 19 (22) ◽  
pp. 3669-3683
Author(s):  
I. V. DOBROVOLSKA ◽  
R. S. TUTIK
Keyword(s):  
Perturbation Theory ◽  
Gordon Equation ◽  
Bound State ◽  
Perturbation Expansions ◽  
Screened Coulomb Potentials ◽  
Lorentz Scalar ◽  
Klein Gordon ◽  
Bound State Problem ◽  
Klein Gordon Equation ◽  
Coulomb Potentials

The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the radial Klein–Gordon equation with attractive screened Coulomb potentials, contained time-component of a Lorentz four-vector and a Lorentz-scalar term, is developed. Based upon ℏ-expansions and new quantization conditions a novel procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and excited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues for the Hulthén potential containing the vector part as well as the scalar component are considered.

scholarly journals SECOND-ORDER CORRECTIONS TO THE NONCOMMUTATIVE KLEIN–GORDON EQUATION WITH A COULOMB POTENTIAL

2011 ◽  
Vol 26 (23) ◽  
pp. 4133-4144 ◽  
Author(s):  
SLIMANE ZAIM ◽  
LAMINE KHODJA ◽  
YAZID DELENDA
Keyword(s):  
Hydrogen Atom ◽  
Coulomb Potential ◽  
Lamb Shift ◽  
Gordon Equation ◽  
Energy Levels ◽  
Space Time ◽  
Second Order ◽  
Noncommutative Space ◽  
Klein Gordon ◽  
Klein Gordon Equation

We improve the previous study of the Klein–Gordon equation in a noncommutative space–time as applied to the hydrogen atom to extract the energy levels, by considering the second-order corrections in the noncommutativity parameter. Phenomenologically we show that noncommutativity is the source of Lamb shift corrections.

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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