Relativistic Wave Equation for Spin-0 Particles: The Klein-Gordon Equation and Its Applications

1997 ◽  
pp. 1-98
Author(s):  
Walter Greiner
Keyword(s):  
Wave Equation ◽  
Gordon Equation ◽  
Relativistic Wave Equation ◽  
Relativistic Wave ◽  
Klein Gordon ◽  
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.

scholarly journals Klein-Gordon Equation and Wave Function for Free Particle in Rindler Space-Time

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Gordon Equation ◽  
Free Particle ◽  
Space Time ◽  
Spinless Particle ◽  
Relativistic Wave Equation ◽  
Relativistic Wave ◽  
Rindler Space ◽  
Klein Gordon ◽  
Klein Gordon Equation

Klein-Gordon equation is a relativistic wave equation. It treats spinless particle. The wave functioncannot use as a probability amplitude. We made Klein-Gordon equation in Rindler space-time. In this paper,we make free particle’s wave function as the solution of Klein-Gordon equation in Rindler space-time.

scholarly journals Symmetry analysis of the Klein–Gordon equation in Bianchi I spacetimes

2015 ◽  
Vol 12 (03) ◽  
pp. 1550033 ◽  
Author(s):  
A. Paliathanasis ◽  
M. Tsamparlis ◽  
M. T. Mustafa
Keyword(s):  
Wave Equation ◽  
Gordon Equation ◽  
Invariant Solution ◽  
Lie Symmetries ◽  
Conformal Algebra ◽  
Noether Symmetries ◽  
Bianchi I ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this work we perform the symmetry classification of the Klein–Gordon equation in Bianchi I spacetime. We apply a geometric method which relates the Lie symmetries of the Klein–Gordon equation with the conformal algebra of the underlying geometry. Furthermore, we prove that the Lie symmetries which follow from the conformal algebra are also Noether symmetries for the Klein–Gordon equation. We use these results in order to determine all the potentials in which the Klein–Gordon admits Lie and Noether symmetries. Due to the large number of cases and for easy reference the results are presented in the form of tables. For some of the potentials we use the Lie admitted symmetries to determine the corresponding invariant solution of the Klein–Gordon equation. Finally, we show that the results also solve the problem of classification of Lie/Noether point symmetries of the wave equation in Bianchi I spacetime and can be used for the determination of invariant solutions of the wave equation.

scholarly journals Dirac Equation in Cosmological Inertial Frame

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Wave Equation ◽  
Dirac Equation ◽  
Inertial Frame ◽  
Gordon Equation ◽  
Probability Amplitude ◽  
Function Type ◽  
Klein Gordon ◽  
Klein Gordon Equation

Dirac equation is a one order-wave equation. Wave function uses as a probability amplitude in quantum mechanics. We make Dirac Equation from wave function, Type A in cosmological inertial frame.The Dirac equation satisfy Klein-Gordon equation in cosmological inertial frame.

scholarly journals A note on the spectrum of discrete Klein-Gordon s-wave equation with eigenparameter dependent boundary condition

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 449-455 ◽  
Author(s):  
Nimet Coskun ◽  
Nihal Yokus
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Boundary Value Problem ◽  
Gordon Equation ◽  
S Wave ◽  
Klein Gordon ◽  
Complex Sequences ◽  
Quantitative Properties ◽  
Klein Gordon Equation ◽  
Jost Solution

This paper is concerned with the boundary value problem (BVP) for the discrete Klein-Gordon equation ?(an-1?yn-1)+(vn-?)2 yn = 0; n ? N and the boundary condition (?0+?1?)y1+(?0+?1)y0 = 0 where (an),(vn) are complex sequences, ?i, ?i ? C, i=0,1 and ? is a eigenparameter. The paper presents Jost solution, eigenvalues, spectral singularities and states some theorems concerning quantitative properties of the spectrum of this BVP under the condition ?n?N exp(?n?)(|1-an| + |vn|) < ? for ? > 0 and 1/2 ? ? ? 1.

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