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Factorization of commutators: The Wick theorem for coupled operators

1993; Elsevier BV; Volume: 554; Issue: 1 Linguagem: Inglês

10.1016/0375-9474(93)90357-4

1873-1554

Chen Jin-quan, Chen Bing-Qing, Abraham Klein,

Quantum optics and atomic interactions

Factorization formulae are given for commutators between any coupled operators, such as [(A × B)j, (C × D)j′], where J can be the angular momentum or other quantum numbers depending on the underlying symmetry. These formulae are generalizations of the Wick theorem to coupled operators. By using these formulas recursively, the outcome of a commutator involving many coupled operators can be calculated easily without any use of the Clebsch-Gordan coefficients. Some commonly used commutators are listed for reference.