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We exhibit the supersymmetric quantum mechanical structure of the full 3+1 dimensional Dirac equation considering ‘mass’ as a function of coordinates. Its usefulness in solving potential problems is discussed with specific examples. We also discuss the ‘physical’ significance of the supersymmetric states in this formalism.
Quantum matrix elements of the coordinate, momentum and the velocity operator for a spin-1/2 particle moving in a scalar-like potential are calculated. In the large quantum number limit, these matrix elements give classical quantities for a relativistic system with a position-dependent mass. Meanwhile, the Klein-Gordon equation for the spin-0 particle is discussed too. Though the Heisenberg equations...
We present solutions of the Dirac equation with spin symmetry for vector and scalar modified Pöschl–Teller potentials within the framework of an approximation of the centrifugal term. The relativistic energy spectrum is obtained using the Nikiforov–Uvarov method and the two-component spinor wave functions obtained are in terms of the Jacobi polynomials. It is found that there exist only positive energy...
Approximate solutions of the Dirac equation with position-dependent mass are presented for the inversely quadratic Yukawa potential and Coulomb-like tensor interaction by using the asymptotic iteration method. The energy eigenvalues and the corresponding normalized eigenfunctions are obtained in the case of position-dependent mass and arbitrary spin-orbit quantum number k state and approximation on...
The Hellmann potential is simply a superposition of an attractive Coulomb potential −a/r plus a Yukawa potential be−δr/r. The generalized parametric Nikiforov–Uvarov (NU) method is used to examine the approximate analytical energy eigenvalues and two-component wave function of the Dirac equation with the Hellmann potential for arbitrary spin-orbit quantum number κ in the presence of exact spin and...
Using the Lorentz transformation, the Klein–Gordon and Dirac equations with moving potentials are reduced to one standard where the potential is time-independent. As application, the reflection and transmission coefficients are determined by considering the moving step with a constant velocity v. It has been found that R ± T = 1 only at x = vt. The problem of massless (2 + 1) Dirac particle is also...
In this work, we have obtained energy levels and charge radius for the β-stability line nucleus, in relativistic shell model. In this model, we considered a close shell for each nucleus containing double magic number and a single nucleon energy level. Here we have taken 41Ca with a single neutron in the 40Ca core as an illustrative example. Then we have selected the Eckart plus Hulthen potentials...
We derive the relativistic Hamiltonian of hydrogen atom in dynamical non-commutative spaces (DNCS or τ-space). Using this Hamiltonian we calculate the energy shift of the ground state as well the 2P1/2, 2S1/2 levels. In all the cases, the energy shift depends on the dynamical non-commutative parameter τ. Using the accuracy of the energy measurement, we obtain an upper bound for τ. We also study the...
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