Application of the exact quantization rule to the relativistic solution of the rotational Morse potential with pseudospin symmetry

Qiang, Wen-Chao; Zhou, Ru; Gao, Yang

doi:10.1088/1751-8113/40/7/016

Cited by 128 publications

(113 citation statements)

References 18 publications

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“…Over the last few decades a variety of analytical methods such as the supersymmetry method (SUSY) [1], Nikiforov-Uvarov (NU) method [2] and asymptotic iteration method (AIM) [3,4] have been developed to solve for any κ state [8]. These results show that the Exact Quantization Rule can be efficiently used to obtain the exact bound-state solutions for most solvable potentials.…”

Section: Introductionmentioning

confidence: 99%

Arbitrary /-state approximate solutions of the Hulthén potential through the exact quantization rule

2008

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Abstract:In this paper, using the Exact Quantization Rule, we present approximate analytical solutions of the radial Schrödinger equation with non-zero values for the Hulthén potential in the frame of an approximation to the centrifugal potential for any states. The energy levels of all bound states can be easily calculated from the Exact Quantization Rule. Specifically, the normalized analytical wave functions are also obtained. Some energy eigenvalues are numerically calculated and compared with those obtained by other methods such as asymptotic iteration, supersymmetry, numerical integration methods, and the schroedinger Mathematica package.PACS ( IntroductionSince quantum mechanics was first established, the finding of exact solutions has been an important research subject which has attracted much attention in this field, because the exact wave function contains all the necessary information about the quantum system under consideration. Over the last few decades a variety of analytical methods such as the supersymmetry method (SUSY)

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Section: Introductionmentioning

confidence: 99%

Arbitrary /-state approximate solutions of the Hulthén potential through the exact quantization rule

2008

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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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“…On the other hand, some typical physical models have been studied like harmonic oscillator [19,20], Woods-Saxon potential [21,22], Morse potential [23][24][25], Eckart potential [26][27][28], Pöschl-Teller potential [29], Manning-Rosen potential [30], and so forth [31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Generalized Nuclear Woods-Saxon Potential under Relativistic Spin Symmetry Limit

Hamzavi

Rajabi

2013

ISRN High Energy Physics

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Application of the exact quantization rule to the relativistic solution of the rotational Morse potential with pseudospin symmetry

Cited by 128 publications

References 18 publications

Arbitrary /-state approximate solutions of the Hulthén potential through the exact quantization rule

Arbitrary /-state approximate solutions of the Hulthén potential through the exact quantization rule

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

Generalized Nuclear Woods-Saxon Potential under Relativistic Spin Symmetry Limit

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