Analysis of a two level system using differential equations
d[no]/ d t = -noBr + n1Br = (n1- n0)Br
d[n1]/ d t = -n1Br + noBr = (n0- n1)Br
Coupled first order differential equations trial solution n0=Ae-lt , n1=Be-lt
Solve using secular determinant |- Br + l Br | |Br - Br + l |
(- Br + l)2- B 2 r2 = 0 , l = 2Br, l = 0