A new approach to the 1/N-expansion for the Dirac equation

Stepanov, S. S.; Tutik, R. S.

doi:10.1016/0375-9601(92)90154-e

Cited by 9 publications

(9 citation statements)

References 17 publications

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“…This explains the increased interest in the Klein-Gordon (KG) and Dirac wave equations to find exact and analytic solutions for energy spectrum and wavefunctions. As a consequence of the physical importance of exact solutions of relativistic KG wave equation in quantum mechanics, under the influence of strong potentials, an increasing interest in this equation has appeared in the study of quark-antiquark mass spectroscopy [4][5][6], atomic, nuclear, and plasma physics [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Exact Klein-Gordon equation with spatially dependent masses for unequal scalar-vector Coulomb-like potentials

Ikhdair

2009

Eur. Phys. J. A

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We study the effect of spatially dependent mass functions over the solution of the Klein-Gordon equation in the (3 + 1)-dimensions for spinless bosonic particles where the mixed scalar-vector Coulomb-like field potentials and masses are directly proportional and inversely proportional to the distance from force center. The exact bound state energy eigenvalues and the corresponding wave functions of the Klein-Gordon equation for mixed scalar-vector and pure scalar Coulomb-like field potentials are obtained by means of the Nikiforov-Uvarov (NU) method. The energy spectrum is discussed for different scalar-vector potential mixing cases and also for constant mass case.

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Section: Introductionmentioning

confidence: 99%

Exact Klein-Gordon equation with spatially dependent masses for unequal scalar-vector Coulomb-like potentials

Ikhdair

2009

Eur. Phys. J. A

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“…The importance of the Klein-Gordon (KG) and Dirac wave equations with scalar and/or 4-vector potentials arises in many fields of physics . In the framework of the mentioned equations, a scalar or an equally mixed scalar and 4-vector potentials have considerable interest in the study of quarkonium systems [6,[8][9][10]12,[16][17][18][19]. The mixture of 4-vector and scalar potentials has been studied by Long and Robson [20].…”

Section: Introductionmentioning

confidence: 99%

“…Iterative procedures concerning the 1/N expansion technique were introduced to deal with KG and Dirac particles [11]. Stepanove and Tutik [10] who have used the h-expansion procedure in a similar manner to the 1/N expansion procedure. Such procedures are straight forward though rather tedious and suffer from convergence problems in comparison to SLNT [4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Relativistic Shifted- l Expansion Technique for Dirac and Klein-Gordon Equations

Mustafa

Barakat

1998

Commun. Theor. Phys.

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The shifted -l expansion technique (SLET) is extended to solve for Dirac particle trapped in spherically symmetric scalar and/or 4-vector potentials. A parameter λ = 0, 1 is introduced in such a way that one can obtain the Klein-Gordon (KG) bound states from Dirac bound states. The 4-vector Coulomb, the scalar linear, and the equally mixed scalar and 4-vector power-law potentials are used in KG and Dirac equations. Exact numerical results are obtained for the 4-vector Coulomb potential in both KG and Dirac equations. Highly accurate and fast converging results are obtained for the scalar linear and the equally mixed scalar and 4-vector power-law potentials.

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“…The Klein -Gordon ( KG) and the Dirac equations with Lorentz scalar ( added to the mass term) and/or Lorentz vector ( coupled as the 0 -component of the four -vector potential ) potentials are of interest in many branches of physics. For example, Lorentz scalar or equally mixed Lorentz scalar and Lorentz vector potentials have considerable interest in quark -antiquark mass spectroscopy [1][2][3][4][5]. Lorentz vector potentials have great utility in atomic, nuclear, and plasma physics [6,7].…”

Section: Introductionmentioning

confidence: 99%

“…Lorentz vector potentials have great utility in atomic, nuclear, and plasma physics [6,7]. Therefore many attempts have been made to develop approximation techniques to treat relativistic particles in the KG and the Dirac equations [1][2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Perturbed Coulomb potentials in the Klein-Gordon equation via the shifted-lexpansion technique

Barakat¹,

Odeh²,

Mustafa³

1998

J. Phys. A: Math. Gen.

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A shifted -l expansion technique is introduced to calculate the energy eigenvalues for Klein -Gordon (KG) equation with Lorentz vector and/or Lorentz scalar potentials. Although it applies to any spherically symmetric potential, those that include Coulomb -like terms are only considered. Exact eigenvalues for a Lorentz vector or a Lorentz scalar, and an equally mixed Lorentz vector and Lorentz scalar Coulombic potentials are reproduced. Highly accurate and rapidly converging ground -state energies for Lorentz vector Coulomb with a Lorentz vector or a Lorentz scalar linear potential, V (r) = −A 1 /r + kr, and V (r) = −A 1 /r and S(r) = kr, respectively, are obtained. Moreover, a simple straightforward closed -form solution for a KGparticle in Coulombic Lorentz vector and Lorentz scalar potentials is presented in appendix A.

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A new approach to the 1/N-expansion for the Dirac equation

Cited by 9 publications

References 17 publications

Exact Klein-Gordon equation with spatially dependent masses for unequal scalar-vector Coulomb-like potentials

Exact Klein-Gordon equation with spatially dependent masses for unequal scalar-vector Coulomb-like potentials

Relativistic Shifted- l Expansion Technique for Dirac and Klein-Gordon Equations

Perturbed Coulomb potentials in the Klein-Gordon equation via the shifted-lexpansion technique

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