In this paper, after presenting the hyperbolic quaternion formalism, an alternative representational method is proposed for the formulation of classical and generalized electromagnetism in the case of the existence of magnetic monopoles and massive photons. Maxwell's equations and relevant field equations are derived in compact, simpler and elegant forms. These equations are compared with their vectorial, complex quaternionic, dual quaternionic and octonionic representations.
Mathematics Subject Classification (2000). 00A79, 8A25, 17D99.
We investigated the analytical [Formula: see text]-wave solutions of Dirac equation for trigonometric Pöschl–Teller (PT) potential under the pseudospin symmetry condition. The energy eigenvalues equation and corresponding wave functions are obtained by using the Nikiforov–Uvarov (NU) method. The energy bound states are also calculated numerically.
Bound state solutions of the Dirac equation for the generalized Woods-Saxon potential are examined for arbitrary κ states by using the approximation to the Coulomb and centrifugal potentials in pseudospin symmetry (PSS) and spin symmetry (SS) limits, respectively. The energy eigenvalues and corresponding eigenfunctions are obtained in closed forms. Some numerical examples are given for proton or anti-proton in a nucleus. The correlations between the energy splitting and some parameters of the effective potential in PSS limit are examined for several pseudospin doublets.
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