Singular inverse Sturm-Liouville problems with Hermite pseudospectral methods

Altundag, H.
Taşeli, Hasan
A numerical approximation to recover certain symmetric potentials in the singular inverse Sturm-Liouville problems over (-infinity,infinity) is presented. A Hermite pseudospectral method is employed to cope with the corresponding direct problem on the real line, which is encountered in the iterative procedure proposed for the inverse problem. The usual but unwelcome ill-posed structure of the resulting numerical algorithm has been treated to some extent by the help of a flexible optimization parameter and regularization techniques. The construction of some specific potentials are illustrated to emphasize the effectiveness of the present scheme.


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).
Effective-mass Dirac equation for Woods-Saxon potential: Scattering, bound states, and resonances
AYDOĞDU, OKTAY; Arda, Altug; Sever, Ramazan (2012-04-01)
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 transmissi...
Pseudospin and spin symmetry in Dirac-Morse problem with a tensor potential
AYDOĞDU, OKTAY; Sever, Ramazan (Elsevier BV, 2011-09-14)
Under the conditions of the pseudospin and spin symmetry, approximate analytical solutions of the Dirac-Morse problem with Coulomb-like tensor potential are presented. The energy eigenvalue equations are found and corresponding radial wave functions are obtained in terms of confluent hypergeometric functions. The energy eigenvalues are calculated numerically in the absence and presence of the tensor potential. We also investigate the contribution of the potential parameters to the energy splitting of the ps...
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 ...
Inverse Sturm-Liouville problems with pseudospectral methods
Altundag, H.; Boeckmann, C.; Taşeli, Hasan (2015-07-03)
In this paper a technique to obtain a first approximation for singular inverse Sturm-Liouville problems with a symmetrical potential is introduced. The singularity, as a result of unbounded domain (-infinity, infinity), is treated by considering numerically the asymptotic limit of the associated problem on a finite interval (-L, L). In spite of this treatment, the problem has still an ill-conditioned structure unlike the classical regular ones and needs regularization techniques. Direct computation of eigen...
Citation Formats
H. Altundag and H. Taşeli, “Singular inverse Sturm-Liouville problems with Hermite pseudospectral methods,” EUROPEAN PHYSICAL JOURNAL PLUS, vol. 136, no. 10, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: