Challenging commutator algebra problem in quantum mechanics

[subny]

Homework Statement

Homework Equations

i think the most relevant equations would be some commutator algebra theorems i do not know of !

The Attempt at a Solution

 

[micromass]

What is the definition of $e^{\lambda A}$? Use that.

 

[subny]

you mean this - http://en.wikipedia.org/wiki/Exponential_function#Formal_definition

ok so how to use that here

 

[micromass]

So $e^{\lambda A} = \sum_{n=0}^{+\infty} \frac{\lambda^n A^n}{n!}$

So can you calculate $e^{\lambda A}B$ now? Just multiply the series with B and apply that $AB = BA + cI$.