НАНОСИСТЕМЫ: ФИЗИКА, ХИМИЯ, МАТЕМАТИКА, 2011, 2 (2), С. 15–31
КВАНТОВОЕ КОЛЬЦО С ПРОВОДНИКОМ:МОДЕЛЬ ДВУХЧАСТИЧНОЙ ЗАДАЧИ
Д. А. Еремин(1), И.Ю. Попов(2)
(1)Мордовский государственный университет им. Н. П. Огарева
(2)Санкт-Петербургский государственный университет информационных технологий,
механики и оптики
ereminda@mail.ru, popov1955@gmail.com
Построены операторы, описывающие поведение двух частиц с дельта−взаимодействием на прямой и в кольце. С помощью полученных операторов описана двухчастичная модель проводника с квантовым кольцом. Спектр полученного оператора численно исследован на наличие дополнительных точечных уровней. Проведено сравнение результата (при условии малой интенсивности взаимодействия между частицами) с результатом для аналогичной одночастичной задачи.
Ключевые слова: уравнение Шредингера, симметрические операторы, теория Крейна, самосопряженные расширения, функция Грина.
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