BACKGROUND: I calculated a spin-1/2 ptl. with const magnetic field. I thought that, as time goes by, the spin should align to the direction of the magnetic field, because the energy of that state is lowest energy. but, the spin vector(expectation value) just rotates around the direction of the magnetic field. and even the energy are not changed. (calculated for general initial condition (a,b) ; a^2 + b^2 =1.) MY QUESTION: 1. the alignment of spin is purely an effect of spin interaction? 2. why the conservation of energy(<E>(t)=<E>(t=0)) with external field is not odd? *initial condition is not the energy eigenfuction of external field. I want to know Δt, elapsed time to align to the direction of the magnetic field. It might be related with material's magnetic susceptibility. of course external field too.