najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2026-17-4-415-423najo-1903Research ArticleMATHEMATICSМАТЕМАТИКАOn eigenvalues of the discrete Schrödinger operator on a ladder of a d-dimensional square latticeО собственных значениях дискретного оператора Шрёдингера на лестнице d-мерной квадратной решёткиМуминовМ. И.MuminovM. I.

Mukhiddin I. Muminov

University blv., 15, Samarkand, 140104; Tashkent, 100174

 

mmuminov@mail.ruСадуллаеваМ. С.SadullaevaM. S.

Maftuna S. Sadullaeva

Yasmin street, 11, Samarkand, 140100

bmaftunasadullaeva03@gmail.comSamarkand State University; V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of SciencesUzbekistanSamarkand State Pedagogical instituteUzbekistan202631082026174415423Copyright © Muminov M.I., Sadullaeva M.S., 20262026Муминов М.И., Садуллаева М.С.Muminov M.I., Sadullaeva M.S.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1903

We consider a discrete Schrödinger operator H on a ladder of d-dimensional square lattices with a self-adjoint matrix-valued potential whose entries are the scalars λ and µ. We investigate conditions for the existence of eigenvalues and describe their exact locations in terms of the parameters λ and µ for the cases d = 1 and d = 2.

Рассматривается дискретный оператор Шрёдингера H на лестнице d-мерных квадратных решёток с самосопряжённым матричнозначным потенциалом, элементами которого являются скаляры λ и μ. Исследуются условия существования собственных значений и описывается их точное расположение в зависимости от параметров λ и μ для случаев d=1 и d=2.

 

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The authors declare that there are no conflicts of interest present.