First, thanks for your previous help. It was greatly needed and appreciated.
So we have proved [A,Bn]=nBn-1[A,B]
Next we have: If F(x)= is any Taylor Series expandable function with an appropriate radius of convergence, and A and B satisfy the conditions already stated, show that the operator function F(B) obeys , where .
Using earlier proof
Now the last part: Use prior result to evaluate where L is a constant having units of length.
Would someone be able to verify the second part and the last part?