Ordered product expansions of operators（AB）^±m with arbitrary positive integer

【摘要】 We arrange quantum mechanical operators ■ in their normally ordered product forms by using Touchard polynomials.Moreover,we derive the anti-normally ordered forms of ■ by using special functions as well as Stirling-like numbers together with the general mutual transformation rule between normal and anti-normal orderings of operators.Further,the Q-and P-ordered forms of（QP）^±m are also obtained by using an analogy method.更多还原

【Abstract】 We arrange quantum mechanical operators ■ in their normally ordered product forms by using Touchard polynomials.Moreover,we derive the anti-normally ordered forms of ■ by using special functions as well as Stirling-like numbers together with the general mutual transformation rule between normal and anti-normal orderings of operators.Further,the Q-and P-ordered forms of（QP）^±m are also obtained by using an analogy method.更多还原