Ordering of some boson operator functions
Vladimir V. Mikhailov · Journal of Physics A Mathematical and General · 1983
The problem of normal ordering of the following boson operator functions (a+a + ) m , (a r +a + ) m , (a+N) m , (a 2 +N) m , where N=a + a, is solved explicitly. Simple algebraic methods are used. As an intermediate result the ordering formulae for the symmetrised products of boson operators are presented. There is agreement with earlier results of other authors and generalisation of these results. A new representation of the generalised Stirling numbers used for the ordering of the binomial (a 2 +N) m is given and several principal properties of these numbers are derived.