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Homework Statement
Homework Equations
The Attempt at a Solution
I tried to solve (a), but i don't know which approach is right ((1) or (2)) and how to solve (b).[/B]
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You don't start the problem correctly. The ##S_z = + \hbar/2 \rangle## state is not an eigenstate of the Hamiltonian, so after a time ##T_2##, the state of the system is not ##e^{i E T_2 / \hbar} S_z = + \hbar/2 \rangle##.
In which direction is the magnetic field?H=(e/mc)S * B , Sz and H differ just by a multiplicative constant, so they commute. The Sz eigenstates are also energy eigenstates.
In the problem, megnetic field is Bx direction.In which direction is the magnetic field?
So how can you rewrite ##\mathbf{S} \cdot \mathbf{B}##?In the problem, megnetic field is Bx direction.
Sx * BSo how can you rewrite ##\mathbf{S} \cdot \mathbf{B}##?
You have to express the initial state in terms of the eigenstates of the Hamiltonian.
Don't forget the normalization factor.Sx and H have same eigenstates, so the initial state l+> is lSx+> + lSx>
Don't forget the normalization factor.
But now that the state is expressed in terms of the eigenstates of the Hamiltonian, it should be easy to calculate the time evolution.
Why? This is a very standard problem in QM and illustrates nicely the concept of precession.I think the answer is weird
I replied the answer that i triedWhy? This is a very standard problem in QM and illustrates nicely the concept of precession.
Ok, I had replied before you posted the solution.I replied the answer that i tried
I got it, then how can i approach problem(b) i think the result of first measurement is same with (a)Ok, I had replied before you posted the solution.
There is a problem, as you can clearly see that the prbability you get ranges from 0 to 2. Check again how you calculate the absolute value squared.
The probability of measuring S_{z} = +ħ/2 is indeed given by the same equation, replacing T_{2} by T_{1}. But you already know the measurement result, so you need to figure out what you get at T_{2}.I got it, then how can i approach problem(b) i think the result of first measurement is same with (a)
Result of first measurement at T1 is the same with (a). I should have to get a probability of that state before i get a expectation value as i did in (a).The probability of measuring S_{z} = +ħ/2 is indeed given by the same equation, replacing T_{2} by T_{1}. But you already know the measurement result, so you need to figure out what you get at T_{2}.
By the way, you can simplify the result you get using explicit values for E_{1} and E_{2}.