New Convenient Way for Deriving Exponential Operators' Disentangling Formulas and Their Applications (II)

Abstract

In the preceding paper [Commun. Theor. Phys. 51 (2009) 321] we have recommended a convenient method for disentangling exponential operators in the form of exp{B + C}, trying to find an operator A that satisfies [A, B] = C, and [A,[A,B]] = 0, then from the Baker–Hausdorff formula we have exp{B + C} = exp{B+[A, B]} = eA eB e−A. After arranging eA eB = eB eA eW, the disentangling exp{B + C} = eB eW is obtained. In this work we use this method to two-mode case, especially, derive the normal ordering form of exp[h(a†a + b†b) + ga†b† + kab] without appealing to Lie algebra method.