The Quantum Spectrum of the 2D Dirac Equation with a Coulomb Potential: Power Series Approach

2004 ◽  
Vol 69 (3) ◽  
pp. 161-165 ◽  
Author(s):  
Shi-Hai Dong ◽  
Guo-Hua Sun
Keyword(s):  
Dirac Equation ◽  
Power Series ◽  
Coulomb Potential ◽  
Quantum Spectrum

ON A RESULT CONCERNING THE BEHAVIOR OF A RELATIVISTIC QUANTUM SYSTEM IN THE COSMIC STRING SPACETIME

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1549-1556 ◽  
Author(s):  
V. B. BEZERRA ◽  
GEUSA DE A. MARQUES
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Dirac Equation ◽  
Quantum System ◽  
Relativistic Electron ◽  
Coulomb Potential ◽  
Cosmic String ◽  
Relativistic Quantum

We consider the problem of a relativistic electron in the presence of a Coulomb potential and a magnetic field in the background spacetime corresponding to a cosmic string. We find the solution of the corresponding Dirac equation and determine the energy spectrum of the particle.

Existence and asymptotics of ground states to the nonlinear Dirac equation with Coulomb potential

2021 ◽  
pp. 1-26
Author(s):  
Tianfang Wang ◽  
Wen Zhang ◽  
Jian Zhang
Keyword(s):  
Dirac Equation ◽  
Coulomb Potential ◽  
Ground State ◽  
Continuous Dependence ◽  
Energy Functional ◽  
Ground State Solution ◽  
State Solution ◽  
Nonlinear Dirac Equation ◽  
Relationship Of ◽  
Least Energy

In this paper we study the Dirac equation with Coulomb potential − i α · ∇ u + a β u − μ | x | u = f ( x , | u | ) u , x ∈ R 3 where a is a positive constant, μ is a positive parameter, α = ( α 1 , α 2 , α 3 ), α i and β are 4 × 4 Pauli–Dirac matrices. The Dirac operator is unbounded from below and above so the associate energy functional is strongly indefinite. Under some suitable conditions, we prove that the problem possesses a ground state solution which is exponentially decay, and the least energy has continuous dependence about μ. Moreover, we are able to obtain the asymptotic property of ground state solution as μ → 0 + , this result can characterize some relationship of the above problem between μ > 0 and μ = 0.

scholarly journals Bound state of solution of Dirac-Coulomb problem with spatially dependent mass

Open Physics ◽  
2014 ◽  
Vol 12 (4) ◽  
Author(s):  
Eser Olğar ◽  
Hayder Dhahir ◽  
Haydar Mutaf
Keyword(s):  
Dirac Equation ◽  
Coulomb Potential ◽  
Mass Function ◽  
Bound State ◽  
Asymptotic Iteration Method ◽  
Bound State Solution ◽  
Function Generator ◽  
Dependent Mass ◽  
And Function ◽  
Position Dependent Mass

AbstractThe bound state solution of Coulomb Potential in the Dirac equation is calculated for a position dependent mass function M(r) within the framework of the asymptotic iteration method (AIM). The eigenfunctions are derived in terms of hypergeometric function and function generator equations of AIM.

scholarly journals Relativistic study of the energy-dependent Coulomb potential including Coulomb-like tensor interaction

2012 ◽  
Vol 90 (7) ◽  
pp. 655-660 ◽  
Author(s):  
M. Hamzavi ◽  
S.M. Ikhdair
Keyword(s):  
Dirac Equation ◽  
Quantum Number ◽  
Coulomb Potential ◽  
Iteration Method ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Asymptotic Iteration Method ◽  
Spin Orbit ◽  
Energy Eigenvalues ◽  
Energy Dependent

The exact Dirac equation for the energy-dependent Coulomb (EDC) potential including a Coulomb-like tensor (CLT) potential has been studied in the presence of spin and pseudospin symmetries with arbitrary spin–orbit quantum number, κ. The energy eigenvalues and corresponding eigenfunctions are obtained in the framework of the asymptotic iteration method. Some numerical results are obtained in the presence and absence of EDC and CLT potentials.

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.

THE DIRAC EQUATION IN A PSEUDOSCALAR COULOMB POTENTIAL

2002 ◽  
Vol 17 (30) ◽  
pp. 1961-1963 ◽  
Author(s):  
D. G. C. McKEON ◽  
G. VAN LEEUWEN
Keyword(s):  
Dirac Equation ◽  
Coulomb Potential ◽  
Bound State

We consider solutions to the Dirac equation in the presence of an external pseudoscalar potential V(r) = 1/r. It is found that no normalizable bound state solutions exist.

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