a) For a non-degenerate two-level system electromagnetic field energy flow "out" of atoms is equal to this flow "into" atoms under the conditions of the thermal equilibrium. Show this derivation for a more general two-level system where both levels are degenerate and show that the principle of detailed balance is valid.

b) Derive the relationship between Einstein's A and B coefficients for a non-degenerate two-level system. Show this derivation for a more general two-level system where both levels are degenerate.