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Journal of Physics Conference Series

Analytical treatment of spin-1/2 particle subject to a combination of potentials

C. A. Onate, Oluwatosin Samuel Obaseki, Adewale Folaranmi Lukman, A. Abolanriwa

Published Aug 1, 2019• 2 citations
Publisher

Abstract

Abstract By using the fundamental principles of supersymmetric quantum mechanics methodology and parametric Nikiforov-Uvarov method respectively, we obtained both the positive and negative (spin and pseudospin symmetries) energy equations of the Dirac equation with scalar and vector potentials. The nonrelativistic limit of the spin symmetry was obtained, and this was used to calculate Fisher information for both position space and momentum space respectively. The behaviour of eigenvalue energy with both the angular frequency and equilibrium bond length respectively were studied. Five special cases of the potential under consideration were also studied. Finally, we examined the feature of Fisher information with the angular frequency which was found to obey Heisenberg uncertainty principle.

DOI
10.1088/1742-6596/1299/1/012114

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Abstract By using the fundamental principles of supersymmetric quantum mechanics methodology and parametric Nikiforov-Uvarov method respectively, we obtained both the positive and negative (spin and pseudospin symmetries) energy equations of the Dirac equation with scalar and vector potentials. The nonrelativistic limit of the spin symmetry was obtained, and this was used to calculate Fisher information for both position space and momentum space respectively. The behaviour of eigenvalue energy with both the angular frequency and equilibrium bond length respectively were studied. Five special cases of the potential under consideration were also studied. Finally, we examined the feature of Fisher information with the angular frequency which was found to obey Heisenberg uncertainty principle.
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The solutions to the Dirac equation are obtained in the spin and pseudospin symmetry limits are presented using the parametric Nikiforov-Uvarov (pNU) method with the inversely quadratic Hellman (IQH) potential. In the exact non-relativistic spin symmetry limit, the energy and wave function of the IQH potential are obtained and used to investigate the Shannon information entropy of the system. Numerical results of the relativistic energies of the spin and pseudospin symmetry limits of the Dirac equation with the IQH potential are presented and observed to exhibit degeneracy. Also, the results of the Shannon entropy for six states (n = 0, 1, 2, 3, 4, 5) show that the momentum space wave function and probability density are better localized than the position space wave function. Also, the Bialynicki-Birula and Mycielski (BBM) inequality is verified for the system. Our results are found to be consistent with those previously reported in the literature.
An approximate solution of the Dirac equation for a spin-1/2 particle under the influence of q -deformed hyperbolic Pöschl–Teller potential combined with trigonometric Scarf II non-central potential is studied analytically. It is assumed that the scalar potential equals the vector potential in order to obtain analytical solutions. Both radial and angular parts of the Dirac equation are solved using the Nikiforov–Uvarov method. A relativistic energy spectrum and the relation between quantum numbers can be obtained using this method. Several quantum wave functions corresponding to several states are also presented in terms of the Jacobi Polynomials.
Using the supersymmetric quantum mechanics (SUSY) approach, we obtained analytical approximate solutions to the Dirac equation with an improved Tietz diatomic potential function under spin and pseudospin symmetries. The energy eigenvalues equation and the corresponding wave spinor for the two symmetries have been explicitly obtained. The non relativistic limit of the spin symmetry has been obtained. The solution of Morse, Deng-Fan, and Rosen-Morse were obtained by changing the numerical value of q We have also obtained the thermodynamic properties of a system under the improved Tietz potential function.
The Klein–Gordon equation for spinless particles, as well as the Weyl–Pauli and Dirac equations for particles with spin, may be derived from one information-theoretic principle. Consider a gedanken experiment whereby the mean position of a particle in a central force field is to be estimated by means of one position measurement. An efficient (optimum) estimate obeys a condition of minimum Fisher information, or minimum precision, according to the second law of thermodynamics. When the Fisher information is minimized subject to a constraint on the mean-square kinetic energy for the particle, the solution is a probability law on position whose corresponding wave amplitude obeys the Klein-Gordon equation, the Weyl–Pauli equation, or the Dirac equation, depending on whether scalar (without spin) or vector (with spin) solutions are sought. The minimized Fisher information is proportional to the mean-square kinetic energy, minus the rest energy of the particle.