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

Abstract

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.

Ro-vibrational studies of diatomic molecules in a shifted Deng-Fan oscillator potential

“…Approximate analytical energies from super‐symmetric shape invariance formalism in conjunction with the wave function analysis has produced slightly better eigenvalues. For the same parameter sets, approximate ro‐vibrational states have also been reported through asymptotic iteration scheme along with a Pekeris‐type scheme for the centrifugal term . Additionally, eigenvalues are available from a MATHEMATICA implementation, as quoted in .…”

“…The purpose of this work is to investigate the bound‐state spectra of DF‐type potential for arbitrary quantum numbers , as well as for both low and high states. Although, some decent results are available, there is a need of systematic analysis in terms of accurate eigenvalues, eigenvalues and other relevant quantities, especially for the situations mentioned earlier. For this, we use the generalized pseudospectral method (GPS), which has been very successful for a number of physically important quantum systems, such as, spiked harmonic oscillator, rational, Hulthén, Yukawa, logarithmic, power‐law, Morse potential as well as static and dynamic studies in molecules and atoms (including Rydberg states) and so forth .…”

A Novel Exactly Theoretical Solvable of Bound States of the Dirac-Kratzer-Fues Problem with Spin and Pseudo-Spin Symmetry

“…In relativistic quantum mechanics, one of the interesting problems is to obtain exact solutions of the Klein-Gordon equation (spin zero particle) and Dirac equation (spin ½ particle) at high energy, much interest in providing analytic solutions to the relativistic equations in many fields of Physics and Chemistry for different central and non central potentials [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The quantum structure based to the ordinary canonical commutations relations in both Schrödinger and Heisenberg (the operators are depended on time) pictures, respectively (Natural units (3) here Ĥ denote to the ordinary quantum Hamiltonian operator.…”

“…The quantum structure based to the ordinary canonical commutations relations in both Schrödinger and Heisenberg (the operators are depended on time) pictures, respectively (Natural units (3) here Ĥ denote to the ordinary quantum Hamiltonian operator. In addition, for spin ½ particles described by the Dirac equation, experiment tells us that must satisfy Fermi Dirac statistics obey the restriction of Pauli, which imply to gives the only non-null equal-time anti-commutator for field operators as follows: [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] Revised: 2016-11-16 doi:10.18052/www.scipress.com/IFSL. 10.8 Accepted: 2016-11-30 2016SciPress Ltd., Switzerland Online: 2016 SciPress applies the CC- .…”

Eigensolutions of the Schrödinger equation with a class of Yukawa potentials via supersymmetric approach

“…with any of these exponential-type potentials are obtained using different methods which include: asymptotic iteration method (AIM) [10][11][12][13][14][15][16], Nikiforov-Uvarov (N.U) method [17][18][19][20], exact/ proper quantization rule [21], supersymmetric method [22][23][24][25][26][27], 1/N shifted expansion method [28], etc.…”