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International Journal of Modern Physics A

Exact solutions of Pauli oscillator with Snyder–de Sitter algebra

Belhi Guerira, Mokhtar Falek, Mustafa Moumni, Noureddine Belghar

Published May 10, 2022• 2 citations
Publisher

Abstract

In this work, we study an explicit calculation of the deformed Pauli–Schrödinger oscillator for nonrelativistic charged spin 1/2 particle in momentum space with Snyder–de Sitter model, where the energy eigenvalues are given in their exact forms, and the corresponding radial wave functions are expressed in associated Jacobi polynomials. We have also studied the effect of the spatial deformation parameter on the bound states of our system.

DOI
10.1142/s0217751x22500695

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In this work, we study an explicit calculation of the deformed Pauli–Schrödinger oscillator for nonrelativistic charged spin 1/2 particle in momentum space with Snyder–de Sitter model, where the energy eigenvalues are given in their exact forms, and the corresponding radial wave functions are expressed in associated Jacobi polynomials. We have also studied the effect of the spatial deformation parameter on the bound states of our system.
Spatially quadratic deformation radial momentum of D-dimensional Klein-Gordon equation with three-dimensional Harmonic Oscillator and Inverse Quadratic potential was investigated using Hypergeometric Method. By using appropriate variable transformation, D-Dimensional Klein-Gordon equation for q deformed momentum was reduced into one order dimensional Schrodinger like equation with Pöschl-Teller like potential. The relativistic energy and wave function equations were obtained from the solution of Schrodinger like equation. Then, the relativistic energy and wave function were calculated and visualized using Matlab R2013 software, respectively. The q deformed parameter had the effect to the relativistic energy and wave function. The increase of q deformed parameter causes the increase of energy spectra and the decrease of amplitude.
We study the problem of the relativistic motion of a 1/2-spin particle in an exactly solvable potential, which consists of the harmonic oscillator potential plus a novel angle-dependent potential, The analytic bound state solutions of the Dirac equation for this potential are obtained by using the Nikiforov–Uvarov method. The wave functions of the radial and angle-dependent parts of the Dirac equation are derived in the form of the Laguerre and Jacobi polynomials. The contribution of the angle-dependent potential to the relativistic energy spectra is discussed under the condition that the scalar potential is equal to or minus the vector potential.
Abstract We consider a q -deformed extension of the Duffin–Kemmer–Petiau oscillator (DKPO) for spin-one bosons in two spatial dimensions. The corresponding problem is easily solved algebraically after realization of the q -deformed algebra in terms of operators of the ordinary Bose algebra. For states associated with the spin-projection numbers ± 1 an equivalent equation in Hamiltonian form is obtained where the Hamiltonian is pseudo-Hermitian, supporting the idea that pseudo-Hermitian models are physically relevant. Then, using the spectral method, we derived the exact expressions for the corresponding metric operator and Hermitian Hamiltonian in closed forms Notably, this Hamiltonian is found to be diagonal, thus implying that the transformation we applied to the pseudo-Hermitian Hamiltonian to work it out is a Foldy-Wouthuysen transformation.
The exact bound-state wavefunctions and the corresponding energy equation are calculated for a new generalized harmonic oscillator problem describing a spin-1/2 fermion in 3+1-dimensions, involving scalar, vector, and tensor couplings acting simultaneously within a particular plane of motion. For the scalar and vector coupling, singular harmonic oscillator shapes are considered, such that the singular term is needed to allow analytical solutions for the wavefunctions while preserving binding under adequate conditions. For the tensor sector,the Dirac oscillator potential is employed, which adds another independent binding mechanism to the problem. The exact bound-state solutions are computed by specifically tuning coefficients for an appropriate pair of \textit{Ansätze} for the radial functions, which leads to wavefunctions in terms of generalized Laguerre polynomials. Although the energy equation cannot provide a general expression for the energy spectrum, specific constraints on the quantum numbers as simple functions of the external potential parameters can be derived for it, which determines the conditions for bound solutions to exist, and of what type: particle, antiparticle or both. It is shown that the results can be simply mapped to the spherically symmetric analogue problem, and this is used to show that the general result encompass several previous particular cases of spherically symmetric harmonic oscillator problems in the Dirac equation available in the literature.