1. The problem statement, all variables and given/known data Show that f(a†a)a† = a†f(a†a + 1) Where f is any analytic function and a and a† satisfy commutation relation [a, a†] = 1. 3. The attempt at a solution I have used [a, a†] = aa†-a†a=1 to write the expression like f(a†a)a†= a†f(aa†) but I don't know what to do next. I know that analytic function can be written like f(x)=Ʃ kn(x-x0)2 and that it is infinitely differentiable, but I don't see how can I sucesssfuly apply this, or there some other trick here.