scholarly journals KLEIN–GORDON AND DIRAC PARTICLES IN NONCONSTANT SCALAR-CURVATURE BACKGROUND

2008 ◽  
Vol 23 (10) ◽  
pp. 1613-1626 ◽  
Author(s):  
M. ALIMOHAMMADI ◽  
A. A. BAGHJARY
Keyword(s):  
Transverse Momentum ◽  
Scalar Curvature ◽  
Discrete Spectrum ◽  
Ground State ◽  
State Energy ◽  
Geometrical Properties ◽  
Dirac Equations ◽  
Dirac Particles ◽  
Klein Gordon ◽  
Energy Formula

The Klein–Gordon and Dirac equations are considered in a semiinfinite laboratory (x > 0) in the presence of background metrics ds2 = u2(x)ημν dxμ dxν and ds2 = -dt2 + u2(x)ηij dxi dxj with u(x) = e±gx. These metrics have nonconstant scalar-curvatures. Various aspects of the solutions are studied. For the first metric with u(x) = egx, it is shown that the spectra are discrete, with the ground state energy [Formula: see text] for spin-0 particles. For u(x) = e-gx, the spectrums are found to be continuous. For the second metric with u(x) = e-gx, each particle, depends on its transverse-momentum, can have continuous or discrete spectrum. For Klein–Gordon particles, this threshold transverse-momentum is [Formula: see text], while for Dirac particles it is g/2. There is no solution for u(x) = egx case. Some geometrical properties of these metrics are also discussed.

The effect of parabolic potential on ground state energy and vibration frequency of magnetopolaron in asymmetric Gaussian potential quantum wells

2021 ◽  
Author(s):  
Jing-Hong Mei ◽  
Jing-Lin Xiao ◽  
Yong Sun ◽  
Bin Zhang ◽  
Xiu-Juan Miao ◽  
...  
Keyword(s):  
Quantum Wells ◽  
Semiconductor Lasers ◽  
Vibration Frequency ◽  
Ground State ◽  
State Energy ◽  
Transformation Method ◽  
Gaussian Potential ◽  
Parabolic Potential ◽  
Potential Applications ◽  
Energy Formula

Anisotropy parabolic potential (APP) effects on ground state (GS) energy [Formula: see text] and the vibration frequency (VF) [Formula: see text] of weak-coupled magnetopolaron (MP) in asymmetric Gaussian quantum wells (AGQWs) were investigated using the linear combination operator and unitary transformation method. The obtained results showed that [Formula: see text] and [Formula: see text] were increased by increasing the barrier height [Formula: see text] of AGQWs as well as transverse and longitudinal confined strengths [Formula: see text] and [Formula: see text] of APP and decreased with increase in the asymmetric Gaussian confinement potential (AGCP) range [Formula: see text] and transverse and longitudinal effective confined lengths [Formula: see text] and [Formula: see text] of APP. Thus, the GS energy and VF of MP could be changed by adjusting the confinement parameters of the APP and AGCP. The study of quantum wells’ semiconductor materials has broad potential applications in semiconductor lasers, optoelectronic devices and quantum information.

scholarly journals Effects of extended uncertainty principle on the relativistic Coulomb potential

2021 ◽  
Vol 36 (03) ◽  
pp. 2150018
Author(s):  
B. Hamil ◽  
M. Merad ◽  
T. Birkandan
Keyword(s):  
Uncertainty Principle ◽  
Coulomb Potential ◽  
State Energy ◽  
Bound State ◽  
Wave Functions ◽  
De Sitter ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Relativistic Coulomb ◽  
Extended Uncertainty

The relativistic bound-state energy spectrum and the wave functions for the Coulomb potential are studied for de Sitter and anti-de Sitter spaces in the context of the extended uncertainty principle. Klein–Gordon and Dirac equations are solved analytically to obtain the results. The electron energies of hydrogen-like atoms are studied numerically.

CREATION OF SCALAR AND DIRAC PARTICLES IN THE PRESENCE OF A TIME VARYING ELECTRIC FIELD IN AN ANISOTROPIC UNIVERSE

2002 ◽  
Vol 17 (20) ◽  
pp. 2781-2781
Author(s):  
VÍCTOR M. VILLALBA
Keyword(s):  
Electric Field ◽  
Particle Distribution ◽  
Anisotropic Universe ◽  
Homogeneous Electric Field ◽  
Dirac Equations ◽  
Dirac Particles ◽  
Electric Interaction ◽  
Quasiclassical Limit ◽  
Klein Gordon ◽  
Hamilton Jacobi Equation

We compute the density of scalar and Dirac particles created by a cosmological anisotropic universe1,2 in the presence of a time dependent homogeneous electric field. In order to compute the rate of particles created we apply a quasiclassical approach that has been used successfully in different scenarios3,4. The idea behind the method is the following: First, we solve the relativistic Hamilton-Jacobi equation and, looking at its solutions, we identify positive and negative frequency modes. Second, after separating variables5,6, we solve the Klein-Gordon and Dirac equations and, after comparing with the results obtained for the quasiclassical limit, we identify the positive and negative frequency states. We show that the particle distribution becomes thermal when one neglects the electric interaction.

scholarly journals A Note on the Discrete Spectrum of Gaussian Wells (I): The Ground State Energy in One Dimension

2016 ◽  
Vol 2016 ◽  
pp. 1-4 ◽  
Author(s):  
G. Muchatibaya ◽  
S. Fassari ◽  
F. Rinaldi ◽  
J. Mushanyu
Keyword(s):  
Integral Operator ◽  
Discrete Spectrum ◽  
Ground State Energy ◽  
Ground State ◽  
Momentum Space ◽  
State Energy ◽  
Transcendental Equation ◽  
One Dimension

The ground state energyE0(λ)ofHλ=-d2/dx2-λe-x2is computed for small values ofλby means of an approximation of an integral operator in momentum space. Such an approximation leads to a transcendental equation for whichϵ0(λ)=|E0(λ)|1/2is the root.

scholarly journals Klein–Gordon lower bound to the semirelativistic ground-state energy

2010 ◽  
Vol 374 (19-20) ◽  
pp. 1980-1984 ◽  
Author(s):  
Richard L. Hall ◽  
Wolfgang Lucha
Keyword(s):  
Lower Bound ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Klein Gordon
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