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Register a new userBound-State Solutions of Dirac Equation for Kratzer Potential with Pseudoscalar-Coulomb Term
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We present exact analytical solutions of the Dirac equation in $(1+1)$-dimensions for the generalized Kratzer potential by taking the pseudoscalar interaction term as an attractive Coulomb potential. We study the problem for a particular (spin) symmetry of the Dirac Hamiltonian. After a qualitative analyse, we study the results for some special cases such as Dirac-Coulomb problem in the existence of the pseudoscalar interaction, and the pure Coulomb problem by discussing some points about pseudospin and spin symmetries in one dimension. We also plot some figures representing the dependence of the energy on quantum number, and potential parameters.
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We obtain the quantized momentum eigenvalues, $P_n$, together with space-like coherent eigenstates for the space-like counterpart of the Schru007fodinger equation, the Feinberg-Horodecki equation, with a combined Kratzer potential plus screened coulomb potential which is constructed by temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: the time-dependent modified Kratzer potential and the time-dependent screened Coulomb potential.
The Dirac equation is solved approximately for the Hulthen potential with the pseudospin symmetry for any spin-orbit quantum number $kappa$ in the position-dependent mass background. Solutions are obtained reducing the Dirac equation into a Schr{o}dinger-like differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions.
We study the two-dimensional massless Dirac equation for a potential that is allowed to depend on the energy and on one of the spatial variables. After determining a modified orthogonality relation and norm for such systems, we present an application involving an energy-dependent version of the hyperbolic Scarf potential. We construct closed-form bound state solutions of the associated Dirac equation.
The Dirac equation, with position-dependent mass, is solved approximately for the generalized Hulth{e}n potential with any spin-orbit quantum number $kappa$. Solutions are obtained by using an appropriate coordinate transformation, reducing the effective mass Dirac equation to a Schr{o}dinger-like differential equation. The Nikiforov-Uvarov method is used in the calculations to obtain energy eigenvalues and the corresponding wave functions. Numerical results are compared with those given in the literature. Analytical results are also obtained for the case of constant mass and the results are in good agreement with the literature.
Approximate bound state solutions of the Dirac equation with -deformed Woods-Saxon plus a new generalized ring-shaped potential are obtained for any arbitrary L-state. The energy eigenvalue equation and corresponding two-component wave function are calculated by solving the radial and angular wave equations within a shortcut of the Nikiforov-Uvarov method. The solutions of the radial and polar angular parts of the wave function are expressed in terms of the Jacobi polynomials. A new approximation being expressed in terms of the potential parameters is carried out to deal with the strong singular centrifugal potential term L(L+1)/r^2. Under some limitations, we can obtain solution for the ring-shaped Hulthen potential and the standard usual spherical Woods-Saxon potential (q=1).
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