Derive the motion equation of density matrix

[raeed]

Homework Statement

density matrix : ρ(t)=0.5+0.5*a(t)⋅σ (a is a 3 dimensional vector and σ is paul victor)
H=-μ*σ⋅B (B is a three dimensional magnetic field )
and also assume that in t=0 , ρ(0)=0.5+0.5*a(0)⋅σ

whats is the motion equation of a(t)?

Homework Equations

whats is the motion equation of a(t)?

The Attempt at a Solution

i tried to use dρ/dt=(-i/ħ)*[H,ρ] but it didn't get me anywhere...

 

[George Jones]

Do you know an identity for

$$\left(\vec{C} \cdot \vec{\sigma}\right) \left(\vec{D} \cdot \vec{\sigma}\right) ?$$

 

[raeed]

Do you know an identity for

$$\left(\vec{C} \cdot \vec{\sigma}\right) \left(\vec{D} \cdot \vec{\sigma}\right) ?$$

ohh i totally forgot about this...
so i used it and i got that
da/dt=(2μ/ħ)*(axB)
is that correct?