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Journals / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2017 / Cilt: 7 - Sayı: 3

Boundary values for an eigenvalue problem with a singular potential

Munevver TUZ
Pages
294–300
Publication Date
2022-10-11
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

We show that the two spectrums uniquely identify thepotential function 𝑞(𝑟) in a single Sturm-Liouville equation, and we obtain newKeywords: evidence for the difference in the 𝑞(𝑟) − 𝑞(𝑟̃) of the Hochstadt theorem.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we consider the inverse spectral problem on the interval [0,1].
📊
Key Findings & Data:Thisdetermines the three-dimensional Schrödinger equation with from singularsymmetric potential.
💡
Conclusion & Impact:We show that the two spectrums uniquely identify thepotential function 𝑞(𝑟) in a single Sturm-Liouville equation, and we obtain newKeywords: evidence for the difference in the 𝑞(𝑟) − 𝑞(𝑟̃) of the Hochstadt theorem.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper we consider the inverse spectral problem on the interval [0,1]. Thisdetermines the three-dimensional Schrödinger equation with from singularsymmetric potential. We show that the two spectrums uniquely identify thepotential function 𝑞(𝑟) in a single Sturm-Liouville equation, and we obtain newKeywords: evidence for the difference in the 𝑞(𝑟) − 𝑞(𝑟̃) of the Hochstadt theorem.

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Cite This Article

TUZ, M. (2022). Boundary values for an eigenvalue problem with a singular potential. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 7 - Sayı: 3, 294–300. https://ajindex.com/articles/440673

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References (17)

  1. Guillot, J. C., &Ralston, J. (1988). Inverse spectral theory for a singular Sturm-Liouville operator on [0, 1]. Journal Differential Equations, 76, 353-373
  2. Carlson, R. (1997). A Borg--Levinson theorem for Bessel operators. Pacific Journal of Mathematics, 177, 1-26
  3. Serier, F. (2007). The inverse spectral problem for radial Schrödinger operators on [0,1]. Journal Differential Equations, 235, 101-126
  4. Savchuk, A. M., &Shkalikov, A. A. (2003). SturmLiouville operators with distribution potentials. Transactions of the Moscow Mathematical Society, 143-192
  5. Albeverio, S., Hryniv, R., & Mykytyuk, Y. (2005). Inverse spectral problems for Sturm--Liouville operators in impedance form. Journal Functional Analysis, 222, 143-177
  6. Panakhov, E.S., &Sat, M.(2013). Reconstruction of potential function for SturmLiouville operator with Coulomb potential. Boundary Value Problems, 2013 (1),19
  7. Sat, M.,& Panakhov, E. (2013). Inverse problem for the interior spectral data of the equation of hydrogen atom. Ukrainian Mathematical Journal, 64.11
  8. 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
  9. 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
  10. Borg, G.(1946). Eine Umkehrung der SturmLiouvilleschen Eigenwertaufgabe. Acta Mathematica, 78, 1-96
  11. Poschel, J., &Trubowitz, E.(1987). Inverse Spectral Theory. Academic Press, Orlando
  12. 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
  13. Abramowitz, M., &Stegun, I.(1972). Handbook of Mathematical Functions. Dover, New York
  14. 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
  15. Rundell, W., &Sacks, P.E. (2001). Reconstruction of a radially symmetric potential from two spectral sequences. Journal Mathematical Analysis and Applications, 264:354-381
  16. Teschl, G. (2009). Mathematical Methods in Quantum Mechanics.With Applications to Schrödinger Operators, Graduate Studies in Mathematics, American Mathematical Society, Rhode Island
  17. Panakhov, E., &Yılmazer, R. (2006). On nverse problem for singular Sturm- Liouville opera