# Time-dependent delta-function perturbation

1. Jul 7, 2014

### carllacan

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
, 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. Jul 7, 2014

### TSny

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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