Research ArticleOpen AccessGoogle Scholar indexed
Inverse Spectral Theory for a Singular Sturm Liouville Operator with Coulomb Potential
Department of Mathematics, Firat University, Elazig, Turkey
Department of Mathematics, Adiyaman University, Adiyaman, Turkey
- 1 Department of Mathematics, Firat University, Elazig, Turkey
- 2 Department of Mathematics, Adiyaman University, Adiyaman, Turkey
Advances in Pure Mathematics·Volume 06 (2016)·Pages 41–49·Published 15 January 2016·DOI10.4236/apm.2016.61005
Copy link · social · email
Abstract
We consider the inverse spectral problem for a singular Sturm-Liouville operator with Coulomb potential. In this paper, we give an asymptotic formula and some properties for this problem by using methods of Trubowitz and Poschel.
KeywordsCoulomb PotentialAsymptotic FormulaNormalizing Eigenfunction
- Sturm, C. and Liouville, J. (1837) Extrait d.un m emoire sur le d eveloppement des fonctions en series dont les di erents terms sont assujettis a satisfaire a une m eme equation di er entielle lin eaire, contenant un param etre variable. Journal de Math ematiques Pures et Appliqu ees. Journal de Mathématiques Pures et Appliquées, 2, 220-233.
- Birkhoff, G.D. (1908) Boundary Value and Expansion Problems of Ordinary Linear Differential Equations. Transactions of the American Mathematical Society, 9, 219-231. http://dx.doi.org/10.1090/S0002-9947-1908-1500810-1
- Titchmarsh, E.C. (1946) Eigenfunction Expansions Associated with Second-Order Differential Equations. Vol. 1, Clarendon Press, Oxford.
- Titchmarsh, E.C. (1958) Eigenfunction Expansions Associated with Second-Order Differential Equations. Vol. 2, Clarendon Press, Oxford.
- Levitan, B.M. (1978) On the Determination of the Sturm-Liouville Operator from One and Two Spectra. Mathematics of the USSR Izvestija, 12, 179-193. http://dx.doi.org/10.1070/IM1978v012n01ABEH001844
- Amirov, R.Kh. (1985) Inverse Problem for the Sturm-Liouville Equation with Coulomb Singularity Its Spectra. Kand. Dissertasiya, Baku.
- Topsakal, N. and Amirov, R. (2010) Inverse Problem for Sturm-Liouville Operators with Coulomb Potential Which Have Discontinuity Conditions inside an Interval. Mathematical Physics, Analysis and Geometry, 13, 29-46. http://dx.doi.org/10.1007/s11040-009-9066-y
- Sat, M. and Panakhov, E.S. (2012) Inverse Nodal Problem for Sturm-Liouville Operators with Coulomb Potential. International Journal of Pure and Applied Mathematics, 80, 173-180.
- Sat, M. and Panakhov, E.S. (2013) Reconstruction of Potential Function for Sturm-Liouville Operator with Coulomb Potential. Boundary Value Problems, 2013, Article 49.
- Sat, M. (2014) Half Inverse Problem for the Sturm-Liouville Operator with Coulomb Potential. Applied Mathematics and Information Sciences, 8, 501-504. http://dx.doi.org/10.12785/amis/080207
- Bas, E. and Metin, F. (2013) Fractional Singular Sturm-Liouville Operator for Coulomb Potential. Advances in Difference Equations, Article ID: 300. http://dx.doi.org/10.1186/1687-1847-2013-300
- Blohincev, D.I. (1949) Foundations of Quantum Mechanics. GITTL, Moscow.
- Poeschel, J. and Trubowitz, E. (1987) Inverse Spectral Theory. Academic Press, San Diego.