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Time-dependent delta-function perturbation

  1. Jul 7, 2014 #1
    1. The problem statement, all variables and given/known data
    We have a system whose state can always be expressed as the sum of two states ##\Psi_a## and ##\Psi_b##. the system undergoes a perturbation of the form ##H'=U\delta(t)##, where ##\delta## is the delta-function in time and ##U_{aa} = U_{bb} = 0## and ## U_{ab} = U_{ba}^*##. Find the (time-dependent) coefficients of the system under such perturbation.

    2. Relevant equations
    http://en.wikipedia.org/wiki/Pertur...m_mechanics)#Method_of_variation_of_constants
    image027.gif , where V is ##U##.
    3. The attempt at a solution
    Griffiths (from whose book I got this exercise) suggests treating the delta-function as a limit in a series of rectangles, so I wrote the integral from -B to B and with a constant A in place of ##\delta##, intending to later take the limit when B → 0 and A→∞.

    My solution, however, turns out to be independent of A (before taking limits), so I think it's wrong.

    How would you approach this?

    Thank you for your time.
     
  2. jcsd
  3. Jul 7, 2014 #2

    TSny

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    I think you are right that the integral will not depend on A (or B). So, taking the limit will be easy!

    Your approach looks good to me. What expression(s) did you get after taking the integral from -B to B?
     
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