Solutions of the Klein-Gordon equation with the improved Manning-Rosen potential energy model in D dimensions

2014 ◽  
Vol 129 (4) ◽  
Author(s):  
Xiao-Yu Chen ◽  
Tao Chen ◽  
Chun-Sheng Jia
Keyword(s):  
Potential Energy ◽  
Gordon Equation ◽  
Energy Model ◽  
Klein Gordon ◽  
Rosen Potential ◽  
Klein Gordon Equation

scholarly journals Derivation of a Relativistic Wave Equation more Profound than Dirac’s Relativistic Wave Equation

2018 ◽  
Vol 10 (6) ◽  
pp. 102
Author(s):  
Koshun Suto
Keyword(s):  
Wave Equation ◽  
Hydrogen Atom ◽  
Dirac Equation ◽  
Potential Energy ◽  
Gordon Equation ◽  
Relativistic Wave Equation ◽  
Relativistic Wave ◽  
Departure Point ◽  
Klein Gordon ◽  
Klein Gordon Equation

The author has previously derived an energy-momentum relationship applicable in a hydrogen atom. Since this relationship is taken as a departure point, there is a similarity with the Dirac’s relativistic wave equation, but an equation more profound than the Dirac equation is derived. When determining the coefficients  and β of the Dirac equation, Dirac assumed that the equation satisfies the Klein-Gordon equation. The Klein-Gordon equation is an equation which quantizes Einstein's energy-momentum relationship. This paper derives an equation similar to the Klein-Gordon equation by quantizing the relationship between energy and momentum of the electron in a hydrogen atom. By looking to the Dirac equation, it is predicted that there is a relativistic wave equation which satisfies that equation, and its coefficients are determined. With the Dirac equation it is necessary to insert a term for potential energy into the equation when describing the state of the electron in a hydrogen atom. However, in this paper, a potential energy term is not introduced into the relativistic wave equation. Instead, potential energy is incorporated into the equation by changing the coefficient  of the Dirac equation.

Approximate solutions of Klein—Gordon equation with improved Manning—Rosen potential in D -dimensions using SUSYQM

2014 ◽  
Vol 23 (12) ◽  
pp. 120303 ◽  
Author(s):  
A. N. Ikot ◽  
H. Hassanabadi ◽  
H. P. Obong ◽  
Y. E. Chad Umoren ◽  
C. N. Isonguyo ◽  
...  
Keyword(s):  
Gordon Equation ◽  
Approximate Solutions ◽  
Klein Gordon ◽  
Rosen Potential ◽  
Klein Gordon Equation
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