We show that application of the methods of the quantum theory of angular momentum enables one to obtain frequency equations for vibrational modes of uniform isotropic elastic sphere, cylindrical rod, and infinite plate and results in a natural classification of these modes. We discuss how these models can be applied to describe vibrations of metal nanoparticles and semiconductor nanocrystals.

Keywords: quantum theory of angular momentum, theory of elasticity, vibrational modes, metal nanoparticles, semiconductor nanocrystals, nanorods, nanoplatelets PACS: 03.65.−w, 46.40.-p, 46.70.−p (all) DOI: 10.3367/UFNe.2019.04.038562 URL: https://ufn.ru/en/articles/2020/1/d/ 000537855600004 2-s2.0-85085128505 2020PhyU...63...57G Citation: Goupalov S V "Classical problems with the theory of elasticity and the quantum theory of angular momentum" Phys. Usp. 63 57–65 (2020) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 24th, February 2019, revised: 8th, April 2019, accepted: 17th, April 2019 Оригинал: Гупалов С В «Классические задачи теории упругости и квантовая теория углового момента» УФН 190 63–72 (2020); DOI: 10.3367/UFNr.2019.04.038562