Boundary values for an eigenvalue problem with a singular potential
DOI:
https://doi.org/10.11121/ijocta.01.2017.00507Keywords:
Spectrum, invers problem, eigenvalue, second-order differential equation.Abstract
In this paper we consider the inverse spectral problem on the interval [0,1]. This determines the three-dimensional Schrödinger equation with from singular symmetric potential. We show that the two spectrums uniquely identify the potential function q(r) in a single Sturm-Liouville equation, and we obtain new evidence for the difference in the q(r)-q(r)of the Hochstadt theorem.
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Guillot, J. C., Ralston, J. (1988). Inverse spectral theory for a singular Sturm-Liouville operator on [0, 1]. Journal Differential Equations, 76 , 353-373.
Carlson, R. (1997). A Borg--Levinson theorem for Bessel operators. Pacific Journal of Mathematics, 177, 1-26.
Serier, F. (2007). The inverse spectral problem for radial Schrödinger operators on [0,1]. Journal Differential Equations, 235, 101-126.
Savchuk, A. M., Shkalikov, A. A. (2003). Sturm-Liouville operators with distribution potentials. Transactions of the Moscow Mathematical Society, 143-192.
Albeverio, S., Hryniv, R., Mykytyuk, Y. (2005). Inverse spectral problems for Sturm--Liouville operators in impedance form. Journal Functional Analysis, 222, 143-177.
Panakhov, E.S., Sat, M.(2013). Reconstruction of potential function for SturmLiouville operator with Coulomb potential. Boundary Value Problems, 2013 (1),19.
Sat, M., Panakhov, E. (2013). Inverse problem for the interior spectral data of the equation of hydrogen atom. Ukrainian Mathematical Journal, 64.11.
Zhornitskaya, L. A., Serov, V. S. (1994). Inverse eigenvalue problems for a singular Sturm- Liouville operator on [0,1]. Inverse Problems, 10:4, 975-987.
Gough, D. (1990). Comments on helioseismic inference. in Progress of Seismology of the Sun and Stars, Lecture Notes in Physics, Springer-Verlag, Berlin, Vol. 367, pp. 283-318.
Borg, G.(1946). Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Acta Mathematica, 78 , 1-96.
Poschel, J., Trubowitz, E.(1987). Inverse Spectral Theory. Academic Press, Orlando.
Bailey, P. B., Everitt, W. N., Zettl, A.(1991). Computing eigenvalues of singular Sturm-Liouville problems. Results in Mathematics, 20, Nos. 1-2 , 391-423.
Abramowitz, M., Stegun, I.(1972). Handbook of Mathematical Functions. Dover, New York.
Sat, M., Panakhov, E.S. (2013). A uniqueness theorem for Bessel operator from interior spectral data. Abstract and Applied Analysis, Vol. 2013. Hindawi Publishing Corporation.
Rundell, W., Sacks, P.E. (2001). Reconstruction of a radially symmetric potential from two spectral sequences. Journal Mathematical Analysis and Applications, 264:354-381.
Teschl, G. (2009). Mathematical Methods in Quantum Mechanics.With Applications to Schrödinger Operators, Graduate Studies in Mathematics, American Mathematical Society, Rhode Island.
Panakhov, E., Yılmazer, R. (2006). On nverse problem for singular Sturm- Liouville operator from two spectra. Ukrainian Mathematical Journal, 58(1),147-154.
Koyunbakan, H., Panakhov, E. (2008). Inverse problem for a snguler differential operator. Mathematical and Computer Modelling, 178-185.
Ercan, A., Panakhov, E. (2017). Stability problem for sngular dirac equation system on finite interval. AIP Conference Proceedings, 1798, 020054.
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