Accurate lower and upper bounds of the energy spectrum for the asymmetrical two-well potentials

Trigonometric basis sets are used in a Rayleigh-Ritz variational method for computing two-sided eigenvalue bounds of the Schrödinger equation in one dimension. The method is based on truncating the infinite interval and solving an eigenvalue problem which obeys the von Neumann and the Dirichlet boundary conditions, respectively. Highly accurate numerical results are presented for the asymmetrical two-well oscillators. © 1996 John Wiley & Sons, Inc.
International Journal of Quantum Chemistry


Taşeli, Hasan (Wiley, 1993-01-01)
The eigenvalues of the Schrodinger equation with a polynomial potential are calculated accurately by means of the Rayleigh-Ritz variational method and a basis set of functions satisfying Dirichlet boundary conditions. The method is applied to the well potentials having one, two, and three minima. It is shown, in the entire range of coupling constants, that the basis set of trigonometric functions has the capability of yielding the energy spectra of unbounded problems without any loss of convergence providin...
Exact Pseudospin Symmetric Solution of the Dirac Equation for Pseudoharmonic Potential in the Presence of Tensor Potential
AYDOĞDU, OKTAY; Sever, Ramazan (Springer Science and Business Media LLC, 2010-04-01)
Under the pseudospin symmetry, we obtain exact solution of the Dirac equation for the pseudoharmonic potential in the presence of the tensor potential with arbitrary spin-orbit coupling quantum number kappa. The energy eigenvalue equation of the Dirac particles is found and the corresponding radial wave functions are presented in terms of confluent hypergeometric functions. We investigate the tensor potential dependence of the energy of the each state in the pseudospin doublet. It is shown that degeneracy b...
Concrete description of CD0(K)-spaces as C(X)-spaces and its applications
Ercan, Z (American Mathematical Society (AMS), 2004-01-01)
We prove that for a compact Hausdorff space K without isolated points, CD0(K) and C(K x {0, 1}) are isometrically Riesz isomorphic spaces under a certain topology on K x {0, 1}. Moreover, K is a closed subspace of K x {0, 1}. This provides concrete examples of compact Hausdorff spaces X such that the Dedekind completion of C(X) is B(S) (= the set of all bounded real-valued functions on S) since the Dedekind completion of CD0(K) is B(K) (CD0(K, E) and CDw (K, E) spaces as Banach lattices).
Fastly Converging 2D Solutions of TE-EFIE on Modified Superformula Contours Optimized via Genetic Algorithms
Guler, Sadri; Onol, Can; Ergül, Özgür Salih; SEVER, EMRAH; DİKMEN, FATİH; TUCHKİN, YURY ALEXANDEROVİCH (2017-07-14)
An infinitely smooth parametrical representation with derivatives of all orders is used, resulting into exponentially converging solutions of hyper-singular electric field integral equation (EFIE) in 2D. A version of superformula tailored for this purpose has been subject to optimization of its parameters via genetic algorithms to provide smooth parameterization for a desired boundary in two-dimensional problems. The organization of the hyper-singular kernel and convergence of the solution for EFIE assuming...
Arda, Altug; Sever, Ramazan (2012-09-28)
Exact bound state solutions of the Dirac equation for the Kratzer potential in the presence of a tensor potential are studied by using the Laplace transform approach for the cases of spin- and pseudo-spin symmetry. The energy spectrum is obtained in the closed form for the relativistic as well as non-relativistic cases including the Coulomb potential. It is seen that our analytical results are in agreement with the ones given in the literature. The numerical results are also given in a table for different p...
Citation Formats
H. Taşeli, “Accurate lower and upper bounds of the energy spectrum for the asymmetrical two-well potentials,” International Journal of Quantum Chemistry, vol. 60, no. 2, pp. 641–648, 1996, Accessed: 00, 2021. [Online]. Available: