Asymptotic expansion of Fredholm determinant associated to a family of Friedrichs models arising in quantum mechanics
https://doi.org/10.17586/2220-8054-2025-16-5-586-592
Abstract
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.
Keywords
Friedrichs model,
quantum mechanics,
lattice,
two-particle system,
Fredholm determinant,
eigenvalue,
expansion
Supporting agencies: The authors express their sincere gratitude for the support received from the Foundation for Basic Research of the Republic of Uzbekistan (Grant No. FL-9524115052). We are greatly indebted to the anonymous referees for a number of constructive and useful comments.
About the Authors
T. Rasulov
Bukhara State University
Uzbekistan
Uzbekistan
Tulkin Rasulov – Faculty of Physics, Mathematics and Information Technologies
M. Ikbol str. 11, 200100 Bukhara
G. Umirkulova
Bukhara State University
Uzbekistan
Uzbekistan
Gulhayo Umirkulova – Faculty of Physics, Mathematics and Information Technologies
M. Ikbol str. 11, 200100 Bukhara
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For citations:
Rasulov T., Umirkulova G. Asymptotic expansion of Fredholm determinant associated to a family of Friedrichs models arising in quantum mechanics. Nanosystems: Physics, Chemistry, Mathematics. 2025;16(5):586-592. https://doi.org/10.17586/2220-8054-2025-16-5-586-592
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