Time period of precession of Sx about B

[Apashanka]

Consider an electron for which l=0 is kept in a uniform magnetic field B.
For which the hamiltonian matrix is {μ_BB,0,0,-μ_BB}
now if the electron is in the state 1/√2{1,1}(e.g in the eigenstates of S_x eigenvalue ħ/2}
If this state is time evolved
1/√2{1,0}exp(-iEt/ħ)+1/√2{0,1}exp(iEt/ħ)
where E=μ_BB
The minimum time for the state becomes
1/√2{1,-1}(e.g eigenvalue -ħ/2 of S_x) spin flip of S_x is t=πħ/2E or t=πħ/2μ_BB
Is 2t =T(the time period of precession of S_x about B)??

 

[kuruman]

Examine the time dependence of the expectation value $\langle \Psi_+ | S_x|\Psi_+ \rangle$ where $|\Psi_+ \rangle$ is the time-evolved eigenstate corresponding to eigenvalue $+\hbar/2.$

 

[Apashanka]

Examine the time dependence of the expectation value $\langle \Psi_+ | S_x|\Psi_+ \rangle$ where $|\Psi_+ \rangle$ is the time-evolved eigenstate corresponding to eigenvalue $+\hbar/2.$

Yes it's ħ/2(cos(2μ_BBt/ħ)