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Из истории физики. К 100-летию квантовой механики


Старая квантовая механика Бора и Зоммерфельда с современной точки зрения

†  а, ‡  б, §  в
а Department of Mathematics, College of Arts and Sciences, Howard University, 2141 6th St NW, Washington, DC, 20059, USA
б Landeshauptstadt München, Seminar TMG Universität, Referat für Bildung und Sport, Marienplatz 8, München, 80331, Germany
в School of Mathematical and Statistical Sciences, Arizona State University, P.O. Box 871804, Tempe, AZ, 85287-1804, USA

Мы обсуждаем модель атома Бора и её дальнейшее развитие Зоммерфельдом на основе современного математического аппарата волновой механики. Вывод правил квантования и уровней энергии осуществляется в квазиклассическом приближении. Интегралы, введённые Зоммерфельдом, вычисляются при помощи элементарных методов, и устанавливаются их связи с уравнениями Шрёдингера и Дирака. Историческое развитие и ключевые моменты перехода от классической к квантовой теории обсуждаются с целью разъяснить структуру и значимость старой квантовой механики.

Текст pdf (1,4 Мб)
Приложение: AppendixErus.pdf pdf (250 Кб)
Приложение: EllipsesAnimateSofisticated.nb nb (202 Кб)
Приложение: EllipsesAnimateAu.nb nb (120 Кб)
Приложение: AppendixE.nb nb (76 Кб)
Приложение: BohrAtomMathematica.nb nb (1,5 Мб)
Приложение: С.К. Суслов. Знаменательная дата и место: сто лет назад pdf (12 Мб)
English fulltext is available at DOI: 10.3367/UFNe.2025.08.040014
Ключевые слова: модель Бора, правило квантования Бора—Зоммерфельда, уравнение Шрёдингера, уравнение Дирака, метод ВКБ, формула тонкой структуры, загадка Зоммерфельда, система компьютерной алгебры—Математика, трансурановые элементы
PACS: 01.65.+g, 02.70.−c, 03.65.−w (все)
DOI: 10.3367/UFNr.2025.08.040014
URL: https://ufn.ru/ru/articles/2026/1/e/
Цитата: Барли К, Руффинг А, Суслов С К "Старая квантовая механика Бора и Зоммерфельда с современной точки зрения" УФН 196 83–103 (2026)
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Поступила: 3 июля 2025, 15 августа 2025

English citation: Barley K, Ruffing A, Suslov S K “Old quantum mechanics by Bohr and Sommerfeld from modern perspective” Phys. Usp. 69 74–93 (2026); DOI: 10.3367/UFNe.2025.08.040014

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