Solutions of Dirac equations with the Pöschl-Teller potential

Jia, Chun‐Sheng; Guo, Ping; Yong-feng, Diao; Liu, Yi; Xie, Xu

doi:10.1140/epja/i2007-10486-2

Cited by 83 publications

(62 citation statements)

References 38 publications

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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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mentioning

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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“…If the nuclei have masses m 1 and m 2 , the reduced mass is defined as μ = m 1 m 2 /(m 1 + m 2 ) and in this point the diatomic molecular model can be included to the spin symmetry and pseudospin symmetry concept [36]. Substituting (9) into (8) leads us to obtain a Schrödinger-like equation for the upper component F nκ (r),…”

Section: Spin Symmetry Solutions Of the Hyperbolic Potentialmentioning

confidence: 99%

Approximate Analytical Solutions of the Dirac Equation with the Hyperbolic Potential in the Presence of the Spin Symmetry and Pseudo-spin Symmetry

2009

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By employing a new improved approximation scheme to deal with the centrifugal term and pseudo-centrifugal term, we solve approximately the Dirac equation with the hyperbolic potential for the arbitrary spin-orbit quantum number κ. Under the condition of the spin and pseudospin symmetry, the bound state energy eigenvalues and the associated two-component spinors of the Dirac particle are obtained approximately by using the basic concept of the supersymmetric shape invariance formalism and the function analysis method.

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“…Then one can use methods which were developed to solve non-relativistic equations exactly or approximately, such as factorization and path-integral methods [18][19][20][21][22], the Nikiforov-Uvarov method [23], shape invariance [24,25], asymptotic iteration method [26][27][28][29][30], supersymmetric quantum mechanics [31], and so on. For instance, the Dirac equation was solved for the Morse potential [32][33][34][35][36], the harmonic-oscillator potential [37][38][39], the pseudoharmonic potential [40], the Pöschl-Teller potential [41][42][43][44], the Woods-Saxon potential [45,46], the Eckart potential [47,48], the Coulomb and the Hartmann potentials [49], the Hyperbolic potentials and the Coulomb tensor interaction [50,51], the Rosen-Morse potential [52], the Hulthén potential [53][54][55], the Hulthén potential including the Coulomb-like tensor potential [56], the v 0 tanh 2 (r/d) potential [57], the Coulomb-like tensor potential [58], the modified Hylleraas potential [59], the Manning-Rosen and the generalized Manning-...…”

Section: Introductionmentioning

confidence: 99%

Refined comparison theorems for the Dirac equation with spin and pseudo-spin symmetry in d dimensions

Hall

Zorin

2016

Eur. Phys. J. Plus

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The classic comparison theorem of quantum mechanics states that if two potentials are ordered then the corresponding energy eigenvalues are similarly ordered, that is to say if Va ≤ V b , then Ea ≤ E b . Such theorems have recently been established for relativistic problems even though the discrete spectra are not easily characterized variationally. In this paper we improve on the basic comparison theorem for the Dirac equation with spin and pseudo-spin symmetry in d ≥ 1 dimensions. The graphs of two comparison potentials may now cross each other in a prescribed manner implying that the energy values are still ordered. The refined comparison theorems are valid for the ground state in one dimension and for the bottom of an angular momentum subspace in d > 1 dimensions. For instance in a simplest case in one dimension, the condition Va ≤ V b is replaced by Ua ≤ U b , where Ui(x) = x 0 Vi(t)dt, x ∈ [0, ∞), and i = a or b.

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Solutions of Dirac equations with the Pöschl-Teller potential

Cited by 83 publications

References 38 publications

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

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

Approximate Analytical Solutions of the Dirac Equation with the Hyperbolic Potential in the Presence of the Spin Symmetry and Pseudo-spin Symmetry

Refined comparison theorems for the Dirac equation with spin and pseudo-spin symmetry in d dimensions

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