Solutions of the Dirac Equation for the Davidson Potential

Setare, M. R.; Haidari, S

doi:10.1007/s10773-009-0128-5

Cited by 21 publications

(16 citation statements)

References 26 publications

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“…However to our knowledge there is no report on the path integral treatment for a class of noncentral potentials which are of interest in understanding the nuclear shell structure within the framework of a modified mean field model [17]. These potentials that describe the rotational-vibrational motion of the nuclear system, have the form…”

Section: Introductionmentioning

confidence: 99%

Path Integral Solution for an Angle-Dependent Anharmonic Oscillator

Haouat¹

2012

Commun. Theor. Phys.

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We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making an adequate change of time we were able to separate the angular motion from the radial one. The relative propagator is then exactly calculated. The energy spectrum and the corresponding wave functions are obtained.

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Section: Introductionmentioning

confidence: 99%

Path Integral Solution for an Angle-Dependent Anharmonic Oscillator

Haouat¹

2012

Commun. Theor. Phys.

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“…Furthermore, some authors have investigated the spin symmetry and Pseudospin symmetry under the Dirac equation in the presence and absence of coulomb tensor interaction for some typical potentials such as the Harmonic oscillator potential [16][17][18][19][20][21][22][23][24][25], Coulomb potential [26,27], Woods-Saxon potential [28,29], Morse potential [30][31][32][33][34][35], Eckart potential [36,37], ring-shaped non-spherical harmonic oscillator [38], Pöschl-Teller potential [39][40][41][42][43], three parameter potential function as a diatomic molecule model [44], Yukawa potential [45][46][47][48][49], pseudoharmonic potential [50], Davidson potential [51], Mie-type potential [52], Deng-Fan potential [53], hyperbolic potential [54] and Tietz potential [55].…”

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confidence: 99%

κ state solutions for the fermionic massive spin-½ particles interacting with double ring-shaped Kratzer and oscillator potentials

Oyewumi

Falaye

Onate

et al. 2014

Int. J. Mod. Phys. E

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In recent years, an extensive survey on various wave equations of relativistic quantum mechanics with different types of potential interactions has been a line of great interest. In this regime, special attention has been given to the Dirac equation because the spin-1/2 fermions represent the most frequent building blocks of the molecules and atoms. Motivated by the considerable interest in this equation and its relativistic symmetries (spin and pseudospin) in the presence of solvable potential model, we attempt to obtain the relativistic bound states solution of the Dirac equation with double ring-shaped Kratzer and oscillator potentials under the condition of spin and pseudospin symmetries. The solutions are reported for arbitrary quantum number in a compact form. the analytic bound state energy eigenvalues and the associated upper-and lower-spinor components of two Dirac particles have been found. Several typical numerical results of the relativistic eigenenergies have also been presented. We found that the existence or absence of the ring shaped potential potential has strong effects on the eigenstates of the Kratzer and oscillator particles with a wide band spectrum except for the pseudospin-oscillator particles where there exist a narrow band gap.

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“…In recent years, some authors have investigated the spin symmetry and Pseudospin symmetry under the Dirac equation for some typical potentials such as the Harmonic oscillator potential [22,23,24,25,26,27,28,29,30], Coulomb potential [31,32], Woods-Saxon potential [33,34], Morse potential [35,36,37,38,39,40], Eckart potential [41,42], ring-shaped non-spherical harmonic oscillator [43], Pöschl-Teller potential [44,45,46,47,48], three parameter potential function as a diatomic molecule model [49], Yukawa potential [50,51,52,53,54], pseudoharmonic potential [55], Davidson potential [56], Mie-type potential [57], Deng-Fan potential [58], hyperbolic potential [59], Tietz potential [60] and Rosen-Morse potential [61,62,63].…”

Section: Introductionmentioning

confidence: 99%

Solutions of the Dirac Equation With the Shifted Deng–fan Potential Including Yukawa-Like Tensor Interaction

Yahya

Falaye

Oluwadare

et al. 2013

Int. J. Mod. Phys. E

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By using the Nikiforov-Uvarov method, we give the approximate analytical solutions of the Dirac equation with the shifted Deng-Fan potential including the Yukawa-like tensor interaction under the spin and pseudospin symmetry conditions. After using an improved approximation scheme, we solved the resulting schrödinger-like equation analytically. Numerical results of the energy eigenvalues are also obtained, as expected, the tensor interaction removes degeneracies between spin and pseudospin doublets.

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Solutions of the Dirac Equation for the Davidson Potential

Cited by 21 publications

References 26 publications

Path Integral Solution for an Angle-Dependent Anharmonic Oscillator

Path Integral Solution for an Angle-Dependent Anharmonic Oscillator

κ state solutions for the fermionic massive spin-½ particles interacting with double ring-shaped Kratzer and oscillator potentials

Solutions of the Dirac Equation With the Shifted Deng–fan Potential Including Yukawa-Like Tensor Interaction

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