Exact solution of the N-dimensional generalized Dirac-Coulomb equation

Tutik, R. S.

doi:10.1088/0305-4470/25/8/006

Cited by 17 publications

(23 citation statements)

References 18 publications

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“…It should be noted that in the case of the superposition of the central potentials above K 2 is required to be larger than A 2 1 −A 2 2 otherwise γ becomes imaginary, causing the breakdown of the bound state solution. Moreover, this result agrees with that obtained by Tutik [8] when only the positive energy ( the particle case) solution is considered.…”

Section: Introductionsupporting

confidence: 92%

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Exact Energy Eigenvalues of the Generalized Dirac–Coulomb Equation via a Modified Similarity Transformation

Mustafa

Barakat

1998

Commun. Theor. Phys.

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With the aid of a modified similarity transformation we have obtained exact energy eigenvalues of the generalized Dirac -Coulomb equation. This equation consists of the time component of the Lorentz 4-vector potential V v (r) = −A 1 /r, and a Lorentz scalar potential V s (r) = −A 2 /r. The transformed radial equations are so simple so that their solutions are inferred from the conventional solutions of the Schrödinger -Coulomb equation.

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Section: Introductionsupporting

confidence: 92%

“…Where the negative square root is not possible for it yields a contradiction to Eq(37). Obviously this result is identical with the known Sommerfeld's fine -structure formula [8,9].…”

Section: Introductionsupporting

confidence: 84%

Exact Energy Eigenvalues of the Generalized Dirac–Coulomb Equation via a Modified Similarity Transformation

Mustafa

Barakat

1998

Commun. Theor. Phys.

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“…The Dirac equation with Coulomb-type vector and scalar potentials in 3+1 dimensions has been solved by using SUSY QM [28] and the matrix form of SUSY QM based on intertwining operators [29]. For the D +1-dimensional case it was treated by reducing the uncoupled radial second-order equations to those of the confluent hypergeometric functions [25,26]. In recent works, it has been studied the Dirac equation for the three-dimensional Kepler-Coulomb problem [30], and with Coulomb-type scalar and vector potentials in D+1 dimensions from an su(1, 1) algebraic approach [31].…”

Section: Introductionmentioning

confidence: 99%

SU(1,1)coherent states for Dirac–Kepler–Coulomb problem inD+1dimensions with

2014

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We decouple the Dirac's radial equations in D + 1 dimensions with Coulomb-type scalar and vector potentials through appropriate transformations. We study each of these uncoupled second-order equations in an algebraic way by using an su(1, 1) algebra realization. Based on the theory of irreducible representations, we find the energy spectrum and the radial eigenfunctions. We construct the Perelomov coherent states for the Sturmian basis, which is the basis for the unitary irreducible representation of the su(1, 1) Lie algebra. The physical radial coherent states for our problem are obtained by applying the inverse original transformations to the Sturmian coherent states.

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“…The key idea is that instead of solving Dirac-Coulomb equation directly, one can solve the second-order Dirac equation [16][17][18][19][20][21][22] In what follows we recycle the modified similarity transformation ( used by Mustafa et al [17] ) and obtain exact solutions for the non-Hermitian generalized Dirac and Klein-Gordon Coulomb Hamiltonians. Although this problem might be seen as oversimplified, it offers a benchmark for the yet to be adequately explored non-Hermitian relativistic Hamiltonians.…”

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confidence: 99%

Dirac and Klein Gordon particles in complex Coulombic fields: a similarity transformation

Mustafa

2003

J. Phys. A: Math. Gen.

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The observation that the existence of the amazing reality and discreteness of the spectrum need not necessarily be attributed to the Hermiticity of the Hamiltonian is reemphasized in the context of the non-Hermitian Dirac and Klein-Gordon Hamiltonians. Complex Coulombic potentials are considered.In one of the first explicit studies of the non-Hermitian Schrödinger Hamiltonians, Caliceti et al [1] have considered the imaginary cubic oscillator problem in the context of perturbation theory. They have offered the first rigorous explanation why the spectrum in such a model may be real and discrete. Only many years later, after being quoted as just a mathematical curiosity [2] in the literature, the possible physical relevance of this result reemerged and emphasized [3]. Initiating thereafter an extensive discussion which resulted in the proposal of the so called PT −symmetric quantum mechanics by Bender and Boettcher [4].The spiritual wisdom of the new formalism lies in the observation that the existence of the real spectrum need not necessarily be attributed to the Hermiticity of the Hamiltonian. This observation has offered a sufficiently strong motivation for the continued interest in the complex, non-Hermitian, cubic model which may be understood as a characteristic representation of a very broad class of the so-called pseudo-Hermitian models with real spectra.

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Exact solution of the N-dimensional generalized Dirac-Coulomb equation

Cited by 17 publications

References 18 publications

Exact Energy Eigenvalues of the Generalized Dirac–Coulomb Equation via a Modified Similarity Transformation

Exact Energy Eigenvalues of the Generalized Dirac–Coulomb Equation via a Modified Similarity Transformation

SU(1,1)coherent states for Dirac–Kepler–Coulomb problem inD+1dimensions with

Dirac and Klein Gordon particles in complex Coulombic fields: a similarity transformation

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