Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
The Laguerre pseudospectral method for the reflection symmetric Hamiltonians on the real line
Date
2007-05-01
Author
Taşeli, Hasan
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
281
views
0
downloads
Cite This
Hermite-Weber functions provide a natural expansion basis for the numerical treatment of the Schrodinger equation on the whole real line. For the reflection symmetric Hamiltonians, however, it is shown here that the transformation of the problem over the half line and use of a Laguerre basis is computationally much more efficient in a pseudospectral scheme.
Subject Keywords
Applied Mathematics
,
General Chemistry
URI
https://hdl.handle.net/11511/39200
Journal
JOURNAL OF MATHEMATICAL CHEMISTRY
DOI
https://doi.org/10.1007/s10910-006-9083-z
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
A class of orthogonal polynomials suggested by a trigonometric Hamiltonian : Symmetric states
Taşeli, Hasan (Springer Science and Business Media LLC, 2004-05-01)
A new subclass of the Jacobi polynomials arising in the exact analytical solution of the one-dimensional Schrodinger equation with a trigonometric potential has been introduced. The polynomials which consist of a free parameter are not ultraspherical polynomials and have been simply named the T - polynomials since they are generated by a trigonometric Hamiltonian. In certain sense, it is shown that the T - polynomials can be regarded as a generalisation of the airfoil polynomials or the Chebyshev polynomial...
An alternative series solution to the isotropic quartic oscillator in N dimensions
Taşeli, Hasan (Springer Science and Business Media LLC, 1996-01-01)
The series solution of the N-dimensional isotropic quartic oscillator weighted by an appropriate function which exhibits the correct asymptotic behavior of the wave function is presented. The numerical performance of the solution in Bill's determinant picture is excellent, and yields the energy spectrum of the system to any desired accuracy for the full range of the coupling constant. Furthermore, it converges to the well-known exact solution of the unperturbed harmonic oscillator wave function, when the an...
A class of orthogonal polynomials suggested by a trigonometric Hamiltonian: Antisymmetric states
Taşeli, Hasan (Springer Science and Business Media LLC, 2005-05-01)
This is the second in a series of papers dealing with the sets of orthogonal polynomials generated by a trigonometric Hamiltonian. In the first of this series, a subclass of the Jacobi polynomials denoted by T-n((u)) (x) and referred to as the T - polynomial of the first kind, which arises in the investigation of the symmetric state eigenfunctions of the Hamiltonian under consideration, was examined. Another subclass of the Jacobi polynomials denoted by U ((u))(n) (x) is introduced here representing the ant...
Exact quantization rule to the Kratzer-type potentials: an application to the diatomic molecules
IKHDAİR, SAMEER; Sever, Ramazan (Springer Science and Business Media LLC, 2009-04-01)
For arbitrary values of n and l quantum numbers, we present a simple exact analytical solution of the D-dimensional (D a parts per thousand yen 2) hyperradial Schrodinger equation with the Kratzer and the modified Kratzer potentials within the framework of the exact quantization rule (EQR) method. The exact bound state energy eigenvalues (E (nl) ) are easily calculated from this EQR method. The corresponding normalized hyperradial wave functions (psi (nl) (r)) are also calculated. The exact energy eigenvalu...
A ROBUST ITERATIVE SCHEME FOR SYMMETRIC INDEFINITE SYSTEMS
Manguoğlu, Murat (Society for Industrial & Applied Mathematics (SIAM), 2019-01-01)
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with a relatively small number of negative eigenvalues. The proposed scheme consists of an outer minimum residual (MINRES) iteration, preconditioned by an inner conjugate gradient (CG) iteration in which CG can be further preconditioned. The robustness of the proposed scheme is illustrated by solving indefinite linear systems that arise in t...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
H. Taşeli, “The Laguerre pseudospectral method for the reflection symmetric Hamiltonians on the real line,”
JOURNAL OF MATHEMATICAL CHEMISTRY
, pp. 407–416, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39200.