Suppose you don't assume H'aa = H'bb = 0.(a) Find ca (t) and cb(t) in first-or...

Suppose you don't assume H'aa = H'bb = 0.

(a) Find ca (t) and cb(t) in first-order perturbation theory, for the case ca(0) = 1, cb(0) = 0. Show that |ca(1)(t)|2 + |cb(1)(t)|2 = 1, to first order in H'.

(b) There is a nicer way to handle this problem. Let

Show that

where

So the equations for da and db are identical in structure to Equation 1 (with an extra factor ei➢ tacked onto H').

(c) Use the method in part (b) to obtain ca(t) and cb(t) in first-order perturbation theory, and compare your answer to (a). Comment on any discrepancies.

Equation 1