О собственных значениях и виртуальных уровнях двухчастичного гамильтониана на $d$-мерной решетке
https://doi.org/10.17586/2220-8054-2023-14-3-295-303
Аннотация
Двухчастичный оператор Шредингера $h_\mu(k),$ $k\in\mathbb{T}^d$ (где $\mu>0$, $\mathbb{T}^d$ -- $d$-мерный тор), ассоциированный с гамильтонианом $\mathrm{h}$ системы двух квантовых частиц, движущихся на $d$-мерной решетке, рассматривается как возмущение свободного гамильтониана $h_0(k)$ потенциальным оператором $\mu{\bf v}$ ранга $3^d$. Условия существования собственных значений и виртуальных уровней оператора $h_\mu(k),$ подробно исследованы относительно энергии взаимодействия частиц $\mu$ и полный квазиимпульс системы двух частиц $k\in\mathbb{T}^d$.
Об авторах
М. Э. Муминов
Samarkand State University; V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences
Узбекистан
Узбекистан
А. М. Хуррамов
Samarkand State University
Узбекистан
Узбекистан
И. Н. Бозоров
Samarkand State University; V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences
Узбекистан
Узбекистан
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Рецензия
Для цитирования:
Муминов М.Э., Хуррамов А.М., Бозоров И.Н. О собственных значениях и виртуальных уровнях двухчастичного гамильтониана на $d$-мерной решетке. Наносистемы: физика, химия, математика. 2023;14(3):295-303. https://doi.org/10.17586/2220-8054-2023-14-3-295-303
For citation:
Muminov M.I., Khurramov A.M., Bozorov I.N. On eigenvalues and virtual levels of a two-particle Hamiltonian on a d-dimensional lattice. Nanosystems: Physics, Chemistry, Mathematics. 2023;14(3):295-303. https://doi.org/10.17586/2220-8054-2023-14-3-295-303
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