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<p>Dedicated with great pleasure to Prof. Leonid P. Nizhnik on the occasion of his 90th birthday. We construct and present a detailed study of the self-adjoint operators of momentum and their perturbations by nonlocal potentials on the entire axis with one limit point and on a finite interval. The domain of definition of these perturbed self-adjoint operators is described by extended homogeneous boundary conditions containing not only boundary values of the function but also linear functionals of functions in the entire domain of their definition. The spectral properties of exactly solvable models of this kind are investigated.</p>

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Spectral Analysis of Self-Adjoint Momentum Operators with Nonlocal Potentials

  • 期刊论文

  • 发表日期：

    2025年12月11日

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  • Kamila Dębowska,
  • Irina Nizhnik

摘要

Dedicated with great pleasure to Prof. Leonid P. Nizhnik on the occasion of his 90th birthday. We construct and present a detailed study of the self-adjoint operators of momentum and their perturbations by nonlocal potentials on the entire axis with one limit point and on a finite interval. The domain of definition of these perturbed self-adjoint operators is described by extended homogeneous boundary conditions containing not only boundary values of the function but also linear functionals of functions in the entire domain of their definition. The spectral properties of exactly solvable models of this kind are investigated.