Effective-mass Dirac equation for Woods-Saxon potential: Scattering, bound states, and resonances

Arda, Altug
Sever, Ramazan
Approximate scattering and bound state solutions of the one-dimensional effective-mass Dirac equation with the Woods-Saxon potential are obtained in terms of the hypergeometric-type functions. Transmission and reflection coefficients are calculated by using behavior of the wave functions at infinity. The same analysis is done for the constant mass case. It is also pointed out that our results are in agreement with those obtained in literature. Meanwhile, an analytic expression is obtained for the transmission resonance and it is observed that the expressions for bound states and resonances are equal for the energy values E = +/- m. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4705284]


Effective Mass Quantum Systems with Displacement Operator: Inverse Square Plus Coulomb-Like Potential
Arda, Altug; Sever, Ramazan (2015-10-01)
The Schrodinger-like equation written in terms of the displacement operator is solved analytically for a inverse square plus Coulomb-like potential. Starting from the new Hamiltonian, the effects of the spatially dependent mass on the bound states and normalized wave functions of the "usual" inverse square plus Coulomb interaction are discussed.
Exact solution of effective mass Schrodinger equation for the Hulthen potential
Sever, Ramazan; TEZCAN, CEVDET; Yesiltas, Oezlem; Bucurgat, Mahmut (2008-09-01)
A general form of the effective mass Schrodinger equation is solved exactly for Hulthen potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function.
Effective mass Schrodinger equation for exactly solvable class of one-dimensional potentials
Aktas, Metin; Sever, Ramazan (2008-01-01)
We deal with the exact solutions of Schrodinger equation characterized by position-dependent effective mass via point canonical transformations. The Morse, Poschl-Teller, and Hulthen type potentials are considered, respectively. With the choice of position-dependent mass forms, exactly solvable target potentials are constructed. Their energy of the bound states and corresponding wavefunctions are determined exactly.
Exact solutions of the schrodinger equation with position-dependent effective mass via general point canonical transformation
Tezcan, Cevdet; Sever, Ramazan (2007-10-01)
Exact solutions of the Schrodinger equation are obtained for the Rosen-Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation. The general form of the point canonical transformation is introduced by using a free parameter. Two different forms of mass distributions are used. A set of the energy eigenvalues of the bound states and corresponding wave functions for target potentials are obtained as a function of the free parameter.
Exact solutions of the Schrodinger equation via Laplace transform approach: pseudoharmonic potential and Mie-type potentials
Arda, Altug; Sever, Ramazan (Springer Science and Business Media LLC, 2012-04-01)
Exact bound state solutions and corresponding normalized eigenfunctions of the radial Schrodinger equation are studied for the pseudoharmonic and Mie-type potentials by using the Laplace transform approach. The analytical results are obtained and seen that they are the same with the ones obtained before. The energy eigenvalues of the inverse square plus square potential and three-dimensional harmonic oscillator are given as special cases. It is shown the variation of the first six normalized wave-functions ...
Citation Formats
O. AYDOĞDU, A. Arda, and R. Sever, “Effective-mass Dirac equation for Woods-Saxon potential: Scattering, bound states, and resonances,” JOURNAL OF MATHEMATICAL PHYSICS, pp. 0–0, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/62785.