- #1

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## Homework Statement

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.

## 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 k

_{n}(x-x

_{0})

^{2}and that it is infinitely differentiable, but I don't see how can I sucesssfuly

apply this, or there some other trick here.