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Determine the Einstein relations by upward and downward transition.
While the system is in equilibrium, the upward and downward transition rates should be equal.
N1ρ(ν) B12= N2 ρ(ν) B21+ N2 A21 ........... (1)
Hence ρ(ν) = N2 A21 / N1B12- N2 B21 ........... (2)
The Einstein relations are specified by the equations 3 and 4.
g1B12= g2B21 ........ (3)
A21/B21= 8πhν3/c3........ (4)
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