scholarly journals Chiral Transverse Electromagnetic Standing Waves with E || H in the Dirac Equation and the Spectra of the Hydrogen Atom

10.5772/19709 ◽  
2011 ◽  
Author(s):  
H. Torres-Silva
Keyword(s):  
Hydrogen Atom ◽  
Dirac Equation ◽  
Standing Waves ◽  
Transverse Electromagnetic

scholarly journals Resolution in the Case of the Hydrogen Atom of an Improved Dirac Equation

2020 ◽  
Vol 11 (07) ◽  
pp. 1075-1090
Author(s):  
Claude Daviau​ ◽  
Jacques Bertrand ◽  
Raymond Albert Ng
Keyword(s):  
Hydrogen Atom ◽  
Dirac Equation

Transverse electromagnetic standing waves with E∥B

1988 ◽  
Vol 56 (9) ◽  
pp. 801-806 ◽  
Author(s):  
H. Zaghloul ◽  
H. A. Buckmaster
Keyword(s):  
Standing Waves ◽  
Transverse Electromagnetic

scholarly journals Ground state of the hydrogen atom via Dirac equation in a minimal-length scenario

2013 ◽  
Vol 73 (7) ◽  
Author(s):  
T. L. Antonacci Oakes ◽  
R. O. Francisco ◽  
J. C. Fabris ◽  
J. A. Nogueira
Keyword(s):  
Hydrogen Atom ◽  
Dirac Equation ◽  
Ground State ◽  
Minimal Length

scholarly journals Dirac particle in the external coulomb field on the background of the Lobachevsky–Riemann space models

2021 ◽  
Vol 65 (2) ◽  
pp. 146-157
Author(s):  
E. M. Оvsiyuk ◽  
A. D. Koral’kov
Keyword(s):  
Hydrogen Atom ◽  
Dirac Equation ◽  
Differential Equations ◽  
Exact Solutions ◽  
Coulomb Field ◽  
Dirac Particle ◽  
Riemann Space ◽  
Energy Spectra ◽  
Spaces Of Constant Curvature ◽  
Quantization Rule

The known systems of the radial equations describing the hydrogen atom on the basis of the Dirac equation in the Lobachevsky–Riemann spaces of constant curvature are investigated. In the both geometrical models, the differential equations of second order with six regular singular points are found, and their exact solutions of Frobenius type are constructed. To produce the quantization rule for energy values we use the known condition which separates the transcendental Frobenius solutions. This provides us with the energy spectra that are physically interpretable and are similar to those for the Klein–Fock–Gordon particle in these space models. These spectra are similar to those that previously have appeared in studying the same systems of the equations with the use of the semi-classical approximation.

scholarly journals NEW TREATMENT OF THE NONCOMMUTATIVE DIRAC EQUATION WITH A COULOMB POTENTIAL

2012 ◽  
Vol 27 (19) ◽  
pp. 1250100 ◽  
Author(s):  
LAMINE KHODJA ◽  
SLIMANE ZAIM
Keyword(s):  
Magnetic Field ◽  
Field Equation ◽  
Hydrogen Atom ◽  
Dirac Equation ◽  
Hyperfine Structure ◽  
Coulomb Potential ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
New Treatment

Using the approach of the modified Euler–Lagrange field equation together with the corresponding Seiberg–Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. We then find the noncommutative modification to the energy levels and the possible new transitions. In the nonrelativistic limit a general form of the Hamiltonian of the hydrogen atom is obtained, and we show that the noncommutativity plays the role of spin and magnetic field which gives the hyperfine structure.

scholarly journals Dirac equation in noncommutative space for hydrogen atom

2009 ◽  
Vol 682 (2) ◽  
pp. 235-239 ◽  
Author(s):  
T.C. Adorno ◽  
M.C. Baldiotti ◽  
M. Chaichian ◽  
D.M. Gitman ◽  
A. Tureanu
Keyword(s):  
Hydrogen Atom ◽  
Dirac Equation ◽  
Noncommutative Space

scholarly journals κ-DEFORMED DIRAC EQUATION

2011 ◽  
Vol 26 (15) ◽  
pp. 1103-1115 ◽  
Author(s):  
E. HARIKUMAR ◽  
M. SIVAKUMAR ◽  
N. SRINIVAS
Keyword(s):  
Perturbation Theory ◽  
Hydrogen Atom ◽  
Dirac Equation ◽  
Power Series ◽  
Time Reversal ◽  
Deformation Parameter ◽  
Generalized Uncertainty Principle ◽  
Minkowski Spacetime ◽  
Planck Length ◽  
Conjugation Invariance

We construct a Dirac equation in κ-Minkowski spacetime and analyze its implications. This κ-deformed Dirac equation is expanded as a power series involving derivatives with respect to commutative coordinates and the deformation parameter, a. We show that the κ-deformation breaks the charge conjugation invariance but preserves parity and time reversal. We then study how the hydrogen atom spectrum is modified due to the κ-deformation, applying perturbation theory. Using this, we obtain bounds on the deformation parameter a, which are a few orders higher than the Planck length. We also show that the effects of deformation on the spectrum are distinct from that of Moyal deformation and generalized uncertainty principle.

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