scholarly journals Quantum particle model of free particle solution in one-dimensional Klein-Gordon equation

2019 ◽  
Author(s):  
Teguh Budi Prayitno
Keyword(s):  
Gordon Equation ◽  
Quantum Particle ◽  
Free Particle ◽  
Particle Model ◽  
One Dimensional ◽  
Klein Gordon ◽  
Klein Gordon Equation ◽  
Particle Solution

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.

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 High-Order Energy and Linear Momentum Conserving Methods for the Klein-Gordon Equation

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 200 ◽  
Author(s):  
He Yang
Keyword(s):  
Numerical Methods ◽  
Gordon Equation ◽  
Free Particle ◽  
High Order ◽  
Linear Momentum ◽  
Relativistic Quantum Mechanics ◽  
Optimal Error Estimates ◽  
Numerical Schemes ◽  
Klein Gordon ◽  
Klein Gordon Equation

The Klein-Gordon equation is a model for free particle wave function in relativistic quantum mechanics. Many numerical methods have been proposed to solve the Klein-Gordon equation. However, efficient high-order numerical methods that preserve energy and linear momentum of the equation have not been considered. In this paper, we propose high-order numerical methods to solve the Klein-Gordon equation, present the energy and linear momentum conservation properties of our numerical schemes, and show the optimal error estimates and superconvergence property. We also verify the performance of our numerical schemes by some numerical examples.

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.

ALGEBRAIC APPROACH TO THE KLEIN–GORDON EQUATION WITH HYPERBOLIC SCARF POTENTIAL

2011 ◽  
Vol 20 (01) ◽  
pp. 55-61 ◽  
Author(s):  
SHISHAN DONG ◽  
SHI-HAI DONG ◽  
H. BAHLOULI ◽  
V. B. BEZERRA
Keyword(s):  
Quantum Mechanics ◽  
Exact Solutions ◽  
Gordon Equation ◽  
Algebraic Approach ◽  
Supersymmetric Quantum Mechanics ◽  
Shape Invariance ◽  
One Dimensional ◽  
Scarf Potential ◽  
Klein Gordon ◽  
Klein Gordon Equation

Using the shape invariance approach we obtain exact solutions of one-dimensional Klein–Gordon equation with equal types of scalar and vector hyperbolic Scarf potentials. This is considered in the framework of supersymmetric quantum mechanics method.

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