# Derive the motion equation of density matrix

1. Nov 25, 2014

### raeed

1. The problem statement, all variables and given/known data
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)?
2. Relevant equations
whats is the motion equation of a(t)?

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

2. Nov 25, 2014

### George Jones

Staff Emeritus
Do you know an identity for

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

3. Nov 25, 2014