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Scalar nonlinearities in physics and chemistry
Author(s) -
Heimsoeth Bettina
Publication year - 1990
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560370107
Subject(s) - scalar (mathematics) , hilbert space , physics , linear operators , mathematical physics , nonlinear system , quantum mechanics , classical mechanics , mathematics , mathematical analysis , geometry , bounded function
Abstract Scalar nonlinearities are operators of the form N ( u ) = 〈 Au , u 〉 Bu , where A , B are linear operators, and 〈·,·〉 is the inner product in a Hilbert space ℋ. This paper reviews applications of scalar nonlinearities. We show that operators of the form N ( u ) are found in equations that describe phenomena of classical mechanics, open systems of quantum mechanics, and chemical physics.