Griffith Intro to QM, 1st order perturb theory in time-dep

[tjsgkdms1111]

Homework Statement

ca(0)=1, cb(0)=0
zeroth: ca(t)=1, cb(t)=0
1st: ca(t)=1, cb(t)=i/hbar*integral(H'(t) exp(iwt)) dt
ca^2+cb^2=1 to 1st order of H'.: What does it mean?
it is evidently not 1 at all.

Homework Equations

The Attempt at a Solution

 

[DrClaude]

Homework Statement

ca(0)=1, cb(0)=0
zeroth: ca(t)=1, cb(t)=0
1st: ca(t)=1, cb(t)=i/hbar*integral(H'(t) exp(iwt)) dt
ca^2+cb^2=1 to 1st order of H'.: What does it mean?
it is evidently not 1 at all.

Homework Equations

The Attempt at a Solution

Is this really a homework question, or you don't understand something about TDPT?

While your question is not clear, I get the feeling that you are bothered by the fact that $|c_a|^2 + |c_b|^2 > 1$, but this is indeed the result you get from 1st-order TDPT. You have to go to higher order to resolve this, or take that by conservation of the norm $c_a$ must be modified such that $|c_a|^2 = 1 - |c_b|^2$ (but that only tells you the probability of staying gin the initial state, and not the actual complex coefficient $c_a$).