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Derive the motion equation of density matrix

  1. Nov 25, 2014 #1
    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. jcsd
  3. Nov 25, 2014 #2

    George Jones

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    Do you know an identity for

    $$\left(\vec{C} \cdot \vec{\sigma}\right) \left(\vec{D} \cdot \vec{\sigma}\right) ?$$
     
  4. Nov 25, 2014 #3
    ohh i totaly forgot about this...
    so i used it and i got that
    da/dt=(2μ/ħ)*(axB)
    is that correct?
     
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