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Einstein Coefficients - Laser Beams

  1. Aug 15, 2016 #1
    1. The problem statement, all variables and given/known data
    Assume a two level laser system with no degeneracy (g1 = g2 = 1).
    If [tex]N_2 + N1 = \text{constant}[\tex], show that [tex]B12 = B21[\tex].

    2. Relevant equations
    [tex]\frac{\partial N_1}{\partial t}=-B_{12}\rho(v_{21}N_1[\tex]
    [tex]\frac{\partial N_2}{\partial t}=-B_{21}\rho(v_{21}N_2[\tex]

    3. The attempt at a solution
    I think there might be something up with the signs in the relevant equation, a convention im not observing.

    [tex]\frac{\partial N_1}{\partial t}+\frac{\partial N_2}{\partial t}=\frac{\partial c}{\partial t}[\tex]
    [tex]\frac{\partial N_1}{\partial t}+\frac{\partial N_2}{\partial t}=0[\tex]

    From here I am stuck, where have I gone wrong?
  2. jcsd
  3. Aug 15, 2016 #2
    Also could someone tell me how to fix the latex?
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