Analytic functions of the annihilation operator

Aleksandar Petrovic

Published 2010-01-05, updated 2010-05-13Version 3

A method for construction of analytic function f of the annihilation operator is given for the first time. f(z) is analytic on some compact domain that does not separate the complex plane. A new form of the identity is given, which is well suited for domain of function. Using Runge's polynomial approximation theorem, such a function f of the annihilation operator is defined on the whole domain. The constructed operators are given in terms of dyads formed of Fock states.