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Abstract <p> We study the eigenfunctions of the continuous spectrum of the Hamiltonian of a three-particle system with pairwise interactions. The eigenfunctions are considered as distributions over the angular variables of momentum. This is equivalent to considering linear combinations of solutions to the scattering problem for the Schrödinger equation on the eigensubspace. The key singularities of these distributions are studied in the momentum representation. In the coordinate representation, a uniform asymptotic behavior of these distributions is obtained. </p>

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Eigenfunctions of the continuous spectrum of the Hamiltonian of a three-particle system as distributions over the momentum variable

  • 期刊论文

  • 发表日期：

    2026年7月24日

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  • S. L. Yakovlev

摘要

Abstract

We study the eigenfunctions of the continuous spectrum of the Hamiltonian of a three-particle system with pairwise interactions. The eigenfunctions are considered as distributions over the angular variables of momentum. This is equivalent to considering linear combinations of solutions to the scattering problem for the Schrödinger equation on the eigensubspace. The key singularities of these distributions are studied in the momentum representation. In the coordinate representation, a uniform asymptotic behavior of these distributions is obtained.