Subtle inconsistencies in the straightforward definition of the logarithmic function of annihilation and creation operators and a way to avoid them
Ljubica Davidović, D. Arsenović, Milena Davidović, Dragomir M Davidović · Journal of Physics A Mathematical and Theoretical · 2009
Using the resolution of identity spanned by coherent states of the harmonic oscillator, any entire function of the creation and the annihilation operators and its action on a vector in Hilbert space can be defined directly and simply. We show that such a direct approach applied to non-entire functions and , present in the literature, may lead to errors and contradictions. We elucidate their roots and propose a way to avoid them. We discuss the obtained results.