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Challenging commutator algebra problem in quantum mechanics

  1. Apr 18, 2013 #1
    1. The problem statement, all variables and given/known data

    image.jpg

    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. jcsd
  3. Apr 18, 2013 #2

    micromass

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    What is the definition of ##e^{\lambda A}##? Use that.
     
  4. Apr 18, 2013 #3
  5. Apr 18, 2013 #4

    micromass

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    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##.
     
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