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
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.