# Challenging commutator algebra problem in quantum mechanics

1. Apr 18, 2013

### subny

1. The problem statement, all variables and given/known data

2. Relevant equations

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

3. The attempt at a solution

2. Apr 18, 2013

### micromass

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

3. Apr 18, 2013

### subny

4. Apr 18, 2013

### micromass

Staff Emeritus
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 $AB = BA + cI$.