Algebraic approaches to eigenvalue equations: The Wronskian method

Yurtsever, Ersin
A recently proposed method for the solution of eigenvalue equations is applied to two different model potentials. Considerable improvements are observed if the algebraic requirements of the Wronskian method are enforced over a region instead of at a single point.
Chemical Physics Letters


Pseudospin and Spin Symmetric Solutions of the Dirac Equation: Hellmann Potential, Wei-Hua Potential, Varshni Potential
Arda, Altug; Sever, Ramazan (Walter de Gruyter GmbH, 2014-03-01)
Approximate analytical solutions of the Dirac equation are obtained for the Hellmann potential, the Wei-Hua potential, and the Varshni potential with any K-value for the cases having the Dirac equation pseudospin and spin symmetries. Closed forms of the energy eigenvalue equations and the spinor wave functions are obtained by using the Nikiforov-Uvarov method and some tables are given to see the dependence of the energy eigenvalues on different quantum number pairs (n, K).
Numerical studies of the electronic properties of low dimensional semiconductor heterostructures
Dikmen, Bora; Tomak, Mehmet; Department of Physics (2004)
An efficient numerical method for solving Schrödinger's and Poisson's equations using a basis set of cubic B-splines is investigated. The method is applied to find both the wave functions and the corresponding eigenenergies of low-dimensional semiconductor structures. The computational efficiency of the method is explicitly shown by the multiresolution analysis, non-uniform grid construction and imposed boundary conditions by applying it to well-known single electron potentials. The method compares well wit...
Exact solution of the Dirac equation with the Mie-type potential under the pseudospin and spin symmetry limit
Aydogdu, Oktay; Sever, Ramazan (Elsevier BV, 2010-02-01)
We investigate the exact solution of the Dirac equation for the Mie-type potentials under the conditions of pseudospin and spin symmetry limits. The bound state energy equations and the corresponding two-component spinor wave functions of the Dirac particles for the Mie-type potentials with pseudospin and spin symmetry are obtained. We use the asymptotic iteration method in the calculations. Closed forms of the energy eigenvalues are obtained for any spin-orbit coupling term K. We also investigate the energ...
YURTSEVER, E (Walter de Gruyter GmbH, 1988-08-01)
Different variational schemes for solving the Schrodinger equation are tested for the model potential of Kratzer-Fues. Wavefunctions are analyzed in terms of their global (expectation values) and local properties which are expressed as functions of coordinates. The Rayleigh-Ritz variation almost uniformly produces the most accurate expectation values. However the point properties show qualitatively different behaviour for different regions of the coordinate space. To define the local quality, a set of crite...
Exact solution of the Klein-Gordon equation for the PT-symmetric generalized Woods-Saxon potential by the Nikiforov-Uvarov method
Ikhdair, Sameer M.; Sever, Ramazan (Wiley, 2007-03-01)
The exact solution of the one-dimensional Klein-Gordon equation of the PT-symmetric generalized Woods-Saxon potential is obtained. The exact energy eigenvalues and wavefunctions are derived analytically by using the Nikiforov and Uvarov method. In addition, the positive and negative exact bound states of the s-states are also investigated for different types of complex generalized Woods-Saxon potentials. (C) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Citation Formats
E. Yurtsever, “Algebraic approaches to eigenvalue equations: The Wronskian method,” Chemical Physics Letters, pp. 386–390, 1987, Accessed: 00, 2020. [Online]. Available: