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Exact solutions for extended waves in 1d anharmonic lattices
Author(s) -
Fischer Fred
Publication year - 2001
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/1521-3889(200109)10:9<777::aid-andp777>3.0.co;2-w
Subject(s) - anharmonicity , physics , angular momentum , classical mechanics , exact solutions in general relativity , vibrational energy , constant (computer programming) , power (physics) , quantum mechanics , molecule , computer science , programming language
A cyclic chain of n equal classic particles coupled by anharmonic forces has a set of extended vibrational modes, for which exact solutions are given. This requires for the power law of the forces certain conditions to be fulfilled. Each mode is characterized by a wave number and the undulations of the particles depend on the total energy and on a new constant of motion that formally expresses a kind of angular momentum. Exact solutions for n = 7 with a twelfth power potential are discussed.