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.
The Attempt at a Solution
I have used [a, a†] = aa†-a†a=1 to write the expression like
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.