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 Klein-Gordon Equation and Wave Function in Robertson-Walker and Schwarzschild space-tim

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Wave Equations ◽  
Gordon Equation ◽  
Space Time ◽  
Wave Functions ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Gauge Fixing ◽  
Klein Gordon ◽  
Klein Gordon Equation

In the general relativity theory, we find Klein-Gordon wave functions in Robertson-Walker and Schwarzschild space-time. Specially, this article is that Klein-Gordon wave equations is treated by gauge fixing equations in Robertson-Walker space-time and Schwarzschild space-time.

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 Vibration of Yukawa Potential Dependent Time and Extended Klein-Gordon Equation in Rindler Space-Time

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Gordon Equation ◽  
Yukawa Potential ◽  
Space Time ◽  
Proca Equation ◽  
Rindler Space ◽  
Klein Gordon ◽  
Yukawa Force ◽  
Klein Gordon Equation

Atom’s nucleus force understand by Yukawa potential independent time. We study Yukawa potentialdependent about time. We make Klein-Gordon equation is satisfied by Yukawa potential dependent about time.Yukawa potential satisfy Proca equation or Klein-Gordon equation. If we represent Yukawa potentialdependent time in Rindler space-time, this Yukawa potential satisfy the extended Klein-Gordon equation inRindler space-time. We understand Yukawa force in Rindler space-time.

Klein‐Gordon and Schrödinger equations for a free particle in the rest frame

2020 ◽  
Vol 33 (1) ◽  
pp. 10-12
Author(s):  
V. N. Salomatov
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rest Frame ◽  
Gordon Equation ◽  
Free Particle ◽  
Spinless Particle ◽  
Particle Model ◽  
Helmholtz Equations ◽  
Klein Gordon ◽  
Klein Gordon Equation

A system of two equations is found that has solutions which coincide with the solutions of the Klein‐Gordon equation in the rest frame. This system includes the Schrödinger equation for a free neutral spinless particle. Using the Schrödinger equation as an additional condition for solving the Klein‐Gordon equation in the rest frame leads to two Helmholtz equations. Helmholtz equations can be solved by specifying a particle model and boundary conditions. One of the Helmholtz equations leads to discreteness of the rest masses of relativistic particles.

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