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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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Three-body Algebraic Theory

Three-body Algebraic Theory

(p.72) Chapter 4 Three-body Algebraic Theory
Algebraic Theory of Molecules

F. Iachello

R. D. Levine

Oxford University Press

In the previous chapter we discussed the usual realization of many-body quantum mechanics in terms of differential operators (Schrödinger picture). As in the case of the two-body problem, it is possible to formulate many-body quantum mechanics in terms of algebraic operators. This is done by introducing, for each coordinate r1,r2,... and momentum p1, p2, . . . , boson creation and annihilation operators, b†iα, biα. The index i runs over the number of relevant degrees of freedom, while the index α runs from 1 to n + 1, where n is the number of space dimensions (see note 3 of Chapter 2). The boson operators satisfy the usual commutation relations, which are for i ≠ j, . . . [biα, b†jα´] = 0, [biα, bjα´] = 0,. . . . . .[bjα, b†iα´] = 0, [b†jα, b†iα´] = 0,. . . . . . [biα, b†iα´] = ẟαα´, [biα, b†iα´] = 0, [b†iα, b†iα´] = 0. . . .

Keywords:   bent triatomic molecules, correlation diagram, dipole function, infrared transitions, linearity parameter, multiplicity problem, resonance, stretching vibrations, transition operator

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