Einstein Coefficients - Laser Beams

[Ivor Denham]

Homework Statement

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].

Homework 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]

The Attempt at a Solution

I think there might be something up with the signs in the relevant equation, a convention I am not observing.

[tex]N_1+N_2=c[\tex]
[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]
[tex]-B_{12}\rho(v_{21}N_1+-B_{21}\rho(v_{21}N_2=0[\tex]
[tex]-B_{12}N_1+-B_{21}N_2=0[\tex]

From here I am stuck, where have I gone wrong?[/B]

 

[Ivor Denham]

Also could someone tell me how to fix the latex?