Non-entire functions of creation and annihilation operators and their relation to phase operator

Abstract

On the coherent states vertical bar alpha gt any entire function of creation and annihilation operators may be defined. We show that it is not the case for non-entire functions. Use of vertical bar alpha alpha vertical bar as identity operator for a non-entire function may lead to contradictory results. On the example of the phase operator we show how these possible contradictions may be avoided. On the coherent states |alpha gt any entire function of creation and annihilation operators may be defined. We show that it is not the case for non-entire functions. Use of |alpha alpha| as identity operator for a non-entire function may lead to contradictory results. On the example of the phase operator we show how these possible contradictions may be avoided.