najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2025-16-5-586-592najo-1529Research ArticleMATHEMATICSМАТЕМАТИКАAsymptotic expansion of Fredholm determinant associated to a family of Friedrichs models arising in quantum mechanicsАсимптотическое разложение определенного интеграла, ассоциированного с семейством моделей Фридрихса, возникающих в квантовой механикеhttps://orcid.org/0000-0002-2868-4390РасуловТ. Х.RasulovT.

Tulkin Rasulov – Faculty of Physics, Mathematics and Information Technologies

M. Ikbol str. 11, 200100 Bukhara

rth@mail.ruhttps://orcid.org/0000-0002-6254-413XУмиркуловаГ. Х.UmirkulovaG.

Gulhayo Umirkulova – Faculty of Physics, Mathematics and Information Technologies

M. Ikbol str. 11, 200100 Bukhara

g.h.umirqulova@buxdu.uzBukhara State UniversityUzbekistan202505112025165586592Copyright © Rasulov T., Umirkulova G., 20252025Расулов Т.Х., Умиркулова Г.Х.Rasulov T., Umirkulova G.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/1529

In this paper, we consider a family of Friedrichs models that arise in quantum mechanics and corresponding to the Hamiltonian of a two-particle system on a one-dimensional lattice. The number, location, and existence conditions of eigenvalues of this family were analyzed. An asymptotic expansion for the associated Fredholm determinant in a neighborhood of the origin has been derived.

В данной работе рассматривается семейство моделей Фридрихса, возникающих в квантовой механике, соответствующих гамильтониану двухчастичной системы на одномерной решетке. Проанализировано количество, расположение и условия существования собственных значений этого семейства. Получено асимптотическое разложение соответствующего определителя Фредгольма в окрестности начала координат.

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