Normal Operators

AUGUST STERN

Vargas-Martínez, J. M., H. M. Moya-Cessa

We give the normal and anti-normal order expressions of the number operator to the power $k$ by using the commutation relation between the annihilation and creation operators. We use those expressions to give general formulae for functions of the number operator in normal and anti-normal order.

Shi-Min Xu, Yunhai Zhang, Xing-Lei Xu +2 more

In this paper, we provide a new kind of operator formula for anti-normally and normally ordering bosonic-operator functions in quantum optics, which can help us arrange a bosonic-operator function f ( λ + ν ) in its anti-normal and normal ordering conveniently. Furthermore, mutual transformation formulas between anti-normal ordering and normal ordering, which have good universality, are derived too. Based on these operator formulas, some new differential relations and some useful mathematical integral formulas are easily derived without really performing these integrations.

Pieter Kok

Fan Hong

By virtue of the technique of integration within an ordered product of operators we present a new approach to obtain operators’ normal ordering. We first put operators into their Weyl ordering through the Weyl-Wigner quantization scheme, and then we convert the Weyl ordered operators into normal ordering by virtue of the normally ordered form of the Wigner operator.

Jochen Pade