9. A coherent state of a simple one-dimensional harmonic oscillator is defined as a self-state of the (non-hemitic) operator of annihilation A) = A|A), %3D where A is, in general, a complex number. (a) Prove that |A) = e-lAF/2ea" |0) is a normalized consistent state. (b) Test the minimum uncertainty ratio for such a state (c) Write A) as A) = E(n)n). Show that the distribution of If(n)| is of the type Poisson. Find the most probable value of n, and from here, of E. (d) Show that a consistent state can also be obtained by applying the translation operator et#p/h to the ground state. With the definition of the previous problem, what A corresponds to? Nota: It is suggested to use Cohen's book, volume I, complement GV