scholarly journals ONE-DIMENSIONAL QUASI-RELATIVISTIC PARTICLE IN THE BOX

2013 ◽  
Vol 25 (08) ◽  
pp. 1350014 ◽  
Author(s):  
KAMIL KALETA ◽  
MATEUSZ KWAŚNICKI ◽  
JACEK MAŁECKI
Keyword(s):  
Relativistic Particle ◽  
Massive Particle ◽  
Relativistic Model ◽  
Eigenvalues And Eigenfunctions ◽  
One Dimensional ◽  
Special Cases ◽  
Klein Gordon ◽  
Square Well ◽  
The One ◽  
Root Operator

The eigenvalues and eigenfunctions of the one-dimensional quasi-relativistic Hamiltonian (-ℏ2c2d2/dx2 + m2c4)1/2 + V well (x) (the Klein–Gordon square-root operator with electrostatic potential) with the infinite square well potential V well (x) are studied. Eigenvalues represent energies of a "massive particle in the box" quasi-relativistic model. Approximations to eigenvalues λn are given, uniformly in n, ℏ, m, c and a, with error less than C1ℏca-1 exp (-C2ℏ-1mca)n-1. Here 2a is the width of the potential well. As a consequence, the spectrum is simple and the nth eigenvalue is equal to (nπ/2 - π/8)ℏc/a + O(1/n) as n → ∞. Non-relativistic, zero mass and semi-classical asymptotic expansions are included as special cases. In the final part, some L2 and L∞ properties of eigenfunctions are studied.

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 Gap breathers in the one-dimensional Klein-Gordon diatomic chain

2007 ◽  
Vol 56 (2) ◽  
pp. 1041
Author(s):  
Li Mi-Shan ◽  
Tian Qiang
Keyword(s):  
One Dimensional ◽  
Diatomic Chain ◽  
Klein Gordon ◽  
The One

Comment on ‘Energy profile of the one-dimensional Klein–Gordon oscillator’

2011 ◽  
Vol 84 (3) ◽  
pp. 037001 ◽  
Author(s):  
Abdelmalek Boumali ◽  
Abdelhakim Hafdallah ◽  
Amina Toumi
Keyword(s):  
Energy Profile ◽  
One Dimensional ◽  
Klein Gordon ◽  
The One

The general Lie group and similarity solutions for the one-dimensional Vlasov–Maxwell equations

1985 ◽  
Vol 33 (2) ◽  
pp. 219-236 ◽  
Author(s):  
Dana Roberts
Keyword(s):  
Lie Group ◽  
Maxwell Equations ◽  
Transformation Group ◽  
Spatial Dimension ◽  
Similarity Solutions ◽  
One Dimensional ◽  
Special Cases ◽  
General Similarity ◽  
The One ◽  
The Individual

The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived here for the coupled (nonlinear) Vlasov–Maxwell equations in one spatial dimension. The case of one species in a background is shown to admit a larger group than the multi-species case. Previous exact solutions are shown to be special cases of the above solutions, and many of the new solutions are found to constrain the form of the distribution function much more than, for example, the BGK solutions do. The individual generators of the Lie group are used to find the possible subgroups. Finally, a simple physical argument is given to show that the asymptotic solution (t→∞) for a one-species, one-dimensional plasma is one of the general similarity solutions.

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.

Moments of the first-passage time of a Wiener process with drift between two elastic barriers

1995 ◽  
Vol 32 (4) ◽  
pp. 1007-1013 ◽  
Author(s):  
Marco Dominé
Keyword(s):  
Wiener Process ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
One Dimensional ◽  
Special Cases ◽  
Backward Equation ◽  
The One ◽  
First Passage Problem ◽  
Reflecting Barriers

The first-passage problem for the one-dimensional Wiener process with drift in the presence of elastic boundaries is considered. We use the Kolmogorov backward equation with corresponding boundary conditions to derive explicit closed-form expressions for the expected value and the variance of the first-passage time. Special cases with pure absorbing and/or reflecting barriers arise for a certain choice of a parameter constellation.

scholarly journals The one dimensional infinite square well with variable mass

2014 ◽  
Vol 8 ◽  
pp. 4285-4300
Author(s):  
J.J. Alvarez ◽  
M. Gadella ◽  
L.P. Lara
Keyword(s):  
Variable Mass ◽  
One Dimensional ◽  
Square Well ◽  
The One
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