Alignment of Spin in const magnetic field.

[gispiamp]

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.

 

[azntoon]

I want to know the physical interpretation of this phenomena. ANSWER:1. The alignment of spin is indeed an effect of spin interaction, but it is also affected by external magnetic fields. The strength and direction of the external field will determine how quickly the spin aligns. 2. It is not odd for the energy to remain constant with an external field because the system is in a steady state. The spin is not changing, so the energy does not change either. This is due to the fact that the system is already in its lowest energy state. In order to calculate the elapsed time to alignment, you will need to consider the material's magnetic susceptibility and the strength of the external field. The stronger the external field, the faster the spin will align.