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On the asymptotics of eigenvalues for a Sturm-Liouville problem with symmetric single-well potential

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In this article, Sturm-Liouville problem with one boundary condition including an eigenparameter is considered, and the asymptotic expansion of its eigenparameter is calculated. The problem also has a symmetric single-well potential, which is an important function in quantum mechanics.
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art. no. 20230129
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
  • Department of Mathematics, Karadeniz Technical University, Karadeniz, Turkey
Bibliografia
  • [1] C. Fulton, Two point boundary value problems with eigenvalue parameter contained in the boundary conditions, Proc. R. Soc. Edinb. 77A (1977), 293–308, DOI: https://doi.org/10.1017/S030821050002521X.
  • [2] C. Fulton, Singular eigenvalue problems with eigenvalue parameter contained in the boundary conditions, Proc. R. Soc. Edinb. 87A (1980), 1–34, DOI: https://doi.org/10.1017/S0308210500012312.
  • [3] D. B. Hinton, Eigenfunction expansions for a singular eigenvalue problem with eigenparameter in the boundary condition, SIAM J. Math. Anal. 12 (1981), 572–584, DOI: https://doi.org/10.1137/0512050.
  • [4] J. Walter, Regular eigenvalue problems with eigenvalue parameter in the boundary conditions, Math. Z. 153 (1973), 301–312, DOI: https://doi.org/10.1007/BF01177870.
  • [5] Sh. Akbarpoor, H. Koyunbakan, and A. Dabbaghian, Solving inverse nodal problem with spectral parameter in boundary conditions, Inverse Probl. Sci. Eng. 27 (2019), no. 12, 1790–1801, DOI: https://doi.org/10.1080/17415977.2019.1597871.
  • [6] H. Coşkun and N. Bayram, Asymptotics of eigenvalues for regular Sturm-Liouville problems with eigenvalue parameter in the boundary condition, J. Math. Anal. 306 (2005), no. 2, 548–566, DOI: https://doi.org/10.1016/j.jmaa.2004.10.030.
  • [7] H. Coşkun and A. Kabataş, Asymptotic approximations of eigenfunctions for regular Sturm-Liouville problems with eigenvalue parameter in the boundary condition for integrable potential, Math. Scand. 113 (2013), no. 1, 143–160, DOI: https://doi.org/10.7146/math.scand.a-15486.
  • [8] H. Coşkun and A. Kabataş, Green’ s function of regular Sturm-Liouville problem having eigenparameter in one boundary condition, Turk. J. Math. Comput. Sci. 4 (2016), 1–9, https://dergipark.org.tr/tr/download/article-file/208729.
  • [9] H. Coşkun, A. Kabataş, and E. Başkaya, On Green’ s function for boundary value problem with eigenvalue dependent quadratic boundary condition, Bound. Value Probl. 71 (2017), 1–12. DOI: https://doi.org/10.1186/s13661-017-0802-0.
  • [10] A. Kabataş, On eigenfunctions of Hill’ s equation with symmetric double well potential, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 71 (2022), no. 3, 634–649, DOI: https://doi.org/10.31801/cfsuasmas.974409.
  • [11] A. Kabataş, Eigenfunction and Green’ s function asymptotics for Hill’ s equation with symmetric single-well potential, Ukr. Math. J. 74 (2022), no. 2, 218–231, DOI: https://doi.org/10.1007/s11253-022-02059-5.
  • [12] A. Kabataş, One boundary value problem including a spectral parameter in all boundary conditions, Opuscula Math. 43 (2023), no. 5, 651–661, DOI: https://doi.org/10.7494/OpMath.2023.43.5.651.
  • [13] M. Ashbaugh and R. Benguria, Optimal lower bound for the gap between the first two eigenvalues of one-dimensional Schrödinger operators with symmetric single-well potentials and related results, Proc. Am. Math. Soc. 105 (1989), 419–424, DOI: https://doi.org/10.2307/2046959.
  • [14] D.- Y. Chen and M.- J. Huang, Comparison theorems for the eigenvalue gap of Schrödinger operators on the real line, Ann. Henri Poincaré, 13 (2012), 85–101, DOI: https://doi.org/10.1007/s00023-011-0126-z.
  • [15] H. Coşkun, E. Başkaya and A. Kabataş, Instability intervals for Hill’ s equation with symmetric single-well potential, Ukr. Math. J. 71 (2019), no. 6, 977–983, DOI: https://doi.org/10.1007/s11253-019-01692-x.
  • [16] M. Horvath, On the first two eigenvalues of Sturm-Liouville operators, Proc. Am. Math. Soc. 131 (2002), no. 4, 1215–1224, DOI: https://doi.org/10.1090/S0002-9939-02-06637-6.
  • [17] M. J. Huang, The first instability interval for Hill equations with symmetric single-well potentials, Proc. Am. Math. Soc. 125 (1997), 775–778, DOI: https://doi.org/10.1090/S0002-9939-97-03705-2.
  • [18] M. J. Huang and T. M. Tsai, The eigenvalue gap for one-dimensional Schrodinger operators with symmetric potentials, Proc. R. Soc. Edinb. 139 (2009), 359–366, DOI: https://doi.org/10.1017/S0308210507000388.
  • [19] N. B. Haaser and J. A. Sullivian, Real Analysis, Van Nostrand Reinhold Co., New York, 1991.
  • [20] H. Konwent, P. Machnikowski, and A. Radosz, Dynamics of a hydrogen-bonded linear chain with a new type of one-particle potential, J. Phys. Condens. Matter 8 (1996), 4325–4338, DOI: https://doi.org/10.1088/0953-8984/8/23/022.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).
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Bibliografia
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bwmeta1.element.baztech-6e77bc7e-30ff-497e-b23d-abf3d17374a6
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