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Quntum question

  1. Feb 12, 2007 #1
    1. The problem statement, all variables and given/known data

    I need to find the eigenvectors of the following operator (a+)^2-(a)^2, when (a+), (a) are the creation and the annihilation operators.

    2. Relevant equations



    3. The attempt at a solution
    I tried to put the eigenvectors as sum of eigenvectors of operator N=(a+)(a).Maybe you know some tricks that can simplify the solution?
     
  2. jcsd
  3. Feb 13, 2007 #2
    I think you need to write (a+) and (a) as -d/dy + y and d/dy + y, where [itex]x=\alpha y[/itex], and [tex]\alpha=\left(\frac{\hbar}{\sqrt{mk}}\right)^{1/2}[/tex]. Then write out (a+)^2-(a)^2, and solve as a differential equation.
     
  4. Feb 19, 2007 #3
    Thank you. I will try.
     
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