In any setting, there are many ways to do the calculation wrong and there are a few clever ways to solve the problem. I agree that it is not trivial that thinking in a unappropriate manner will lead to the same result as the simple and clever calculation.But instead, if you say, I KNOW my states, and they have only TWO possible outcomes, of course the problem becomes much simpler and probably they yield the same results, but it's just NOT that trivial, if you think about the details, and that's my whole point.
You wouldn't know the simple and clever calculation if it wasn't in every QM textbook. It appears that it didn't even occur to you how to do the problem EXACTLY. And finally, you cannot justify WHY the states can be written so simply (for a system of utmost delicacy (spins) and with reasonable complexity (non-uniform B-fields)) without referring to your beloved textbooks.In any setting, there are many ways to do the calculation wrong and there are a few clever ways to solve the problem. I agree that it is not trivial that thinking in a unappropriate manner will lead to the same result as the simple and clever calculation.
Very nice and civilized manner indeed.It now is obvious that you are not the bit of an expert who should take this question, so please don't pollute the thread and prevent me from learning from all the other people here. Maybe there's still a chance that somebody will respond after all this unnecessary fight.
Very nice and civilized manner indeed.
If you like the gory details, you may read
Ph. A. Martin and M. Sassoli de Bianchi, "Spin precession revisited", Foundations of Physics Volume 24, Number 10 / October, 1994
Personally, I'd better get out of here.