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Homework Help: Problem from Quantum Optics

  1. Jul 25, 2016 #1
    1. The problem statement, all variables and given/known data
    What is the Expectation value of

    $$\sum_{l=0}^{n} \bra{n} (a\dagger)^l(a)^l\ket{n}$$

    where $$a\dagger$$ and $$a$$ are lowering operators
    2. Relevant equations
    3. The attempt at a solution
    I get the solution as $$\sum_{l=0}^{n} (n)!(n+1)!$$
    But the correct answer is $$\sum_{l=0}^{n} \frac{n!}{(n-l)!}$$
  2. jcsd
  3. Jul 25, 2016 #2
    Sorry I got the answer! please delete this thread
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