Quntum question

  • #1

Homework Statement



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

Homework Equations





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?
 

Answers and Replies

  • #2
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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.
 
  • #3
Thank you. I will try.
 
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