- #1
carllacan
- 274
- 3
Homework Statement
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.
Homework Equations
http://en.wikipedia.org/wiki/Pertur...m_mechanics)#Method_of_variation_of_constants
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.