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Algebraic Theory of Molecules$
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F. Iachello and R. D. Levine

Print publication date: 1995

Print ISBN-13: 9780195080919

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195080919.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 21 June 2021

Summary of Elements of Algebraic Theory

Summary of Elements of Algebraic Theory

Chapter:
(p.21) Chapter 2 Summary of Elements of Algebraic Theory
Source:
Algebraic Theory of Molecules
Author(s):

F. Iachello

R. D. Levine

Publisher:
Oxford University Press
DOI:10.1093/oso/9780195080919.003.0005

Algebraic theory makes use of an algebraic structure. The structure appropriate to ordinary quantum mechanical problems is that of a Lie algebra. We begin this chapter with a brief review of the essential concepts of Lie algebras. The binary operation (“multiplication”) in the Lie algebra is that of taking the commutator. As usual, we denote the commutator by square brackets, [A, B] = AB - BA. A set of operators {X} is a Lie algebra when it is closed under commutation.

Keywords:   anharmonicity, boson operators, commutator, dipole operator, electrical anharmonicities, generators, harmonic limit, invariant operators, line strength, missing labels

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