Spinless particles in screened Coulomb potential

Rao, Nagalakshmi A.; Kagali, B. A.

doi:10.1016/s0375-9601(02)00138-x

Cited by 39 publications

(53 citation statements)

References 5 publications

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“…Note that for this potential there is no explicit form of the energy expression of bound states for Schrödinger [13], KG [16] and also Dirac [11,12] equations.…”

Section: Spin Symmetric Solutionmentioning

confidence: 99%

Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

Ikhdair

Sever

2010

Open Physics

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Abstract:We study the approximate analytical solutions of the Dirac equation for the generalized Woods-Saxon potential with the pseudo-centrifugal term. We apply the Nikiforov-Uvarov method (which solves a second-order linear differential equation by reducing it to a generalized hypergeometric form) to spin-and pseudospin-symmetry to obtain, in closed form, the approximately analytical bound state energy eigenvalues and the corresponding upper-and lower-spinor components of two Dirac particles. The special cases κ = ±1 ( = = 0 -wave) and the non-relativistic limit can be reached easily and directly for the generalized and standard Woods-Saxon potentials. We compare the non-relativistic results with those obtained by others.

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“…Note that for this potential there is no explicit form of the energy expression of bound states for Schrödinger [13], KG [16] and also Dirac [11,12] equations.…”

Section: Spin Symmetric Solutionmentioning

confidence: 99%

Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

Ikhdair

Sever

2010

Open Physics

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“…To our knowledge, only a few analytical results exist concerning a relativistic Yukawa problem [32,33]. These results are moreover obtained by solving one-dimensional Hamiltonians, either Klein-Gordon or Dirac, but not a three-dimensional spinless Salpeter Hamiltonian.…”

Section: Energy Spectrummentioning

confidence: 99%

Semirelativistic Hamiltonians and the Auxiliary Field Method

Silvestre‐Brac

Semay

Buisseret

2009

Int. J. Mod. Phys. A

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Approximate analytical closed energy formulas for semirelativistic Hamiltonians of the form σ p p 2 + m 2 + V (r) are obtained within the framework of the auxiliary field method. This method, which is equivalent to the envelope theory, has been recently proposed as a powerful tool to get approximate analytical solutions of the Schrödinger equation. Various shapes for the potential V (r) are investigated: power-law, funnel, square root, and Yukawa. A comparison with the exact results is discussed in detail.

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“…Although the vector Coulomb potential does not hold relativistic bound-state solutions, its screened version (∼ e −|x|/λ ) is a genuine binding potential and its solutions have been found for fermions [25]. The screened Coulomb potential has also been analyzed with a scalar coupling in the Dirac equation [26] as well as in the Klein-Gordon equation with vector [27] and scalar [28] couplings.…”

Section: Introductionmentioning

confidence: 99%

Bounded solutions of neutral fermions with a screened Coulomb potential

Castro¹

2005

Annals of Physics

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The intrinsically relativistic problem of a fermion subject to a pseudoscalar screened Coulomb plus a uniform background potential in two-dimensional space-time is mapped into a Sturm-Liouville. This mapping gives rise to an effective Morse-like potential and exact bounded solutions are found. It is shown that the uniform background potential determinates the number of bound-state solutions. The behaviour of the eigenenergies as well as of the upper and lower components of the Dirac spinor corresponding to bounded solutions is discussed in detail and some unusual results are revealed. An apparent paradox concerning the uncertainty principle is solved by recurring to the concepts of effective mass and effective Compton wavelength.

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Spinless particles in screened Coulomb potential

Cited by 39 publications

References 5 publications

Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

Semirelativistic Hamiltonians and the Auxiliary Field Method

Bounded solutions of neutral fermions with a screened Coulomb potential

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