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Find the transition probability

  1. Mar 23, 2015 #1
    Applying an operator gif.gif to an initial state gif.gif can cause it to change into a different state gif.gif , if gif.gif is not an eigenstate of gif.gif . The probability for this transition to occur is gif.gif , where gif.gif is called the transition amplitude. Consider the case where the initial state is the gif.gif state of the harmonic oscillator, gif.gif , the final state is the gif.gif state of the harmonic oscillator, gif.gif , and the operator is gif.gif . ( gif.gif is the position operator.) Find the transition probability from gif.gif to gif.gif .


    I really am not even sure where to start......
     
  2. jcsd
  3. Mar 23, 2015 #2
    Look up the eigenfunctions of the harmonic oscillator, operate with the given operator on the initial state, integrate according to the definition of the transition amplitude.
     
  4. Mar 23, 2015 #3
    When you say on the initial state do you mean when psi(n)=1/sqrt(n) a+ psi(n-1) or do you mean psi(2)=1/sqrt(2) a+ psi(1)
     
  5. Mar 24, 2015 #4
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