EINSTEIN'S SPONTANEOUS EMISSION EQUATION AS ANTITONIC PROCESS

In 1917, Albert Einstein published a derivation of Planck's radiation law. He was not satisfied with Planck's derivation because it changed assumptions to obtain the result.
He found that a molecule which is not in the ground state can emit radiation and pass to the next lower state (perhaps the ground condition) with probability:
dW = (Aⁿ_m + Bⁿ_mr)
For equilibrium with the molecular distribution of states at temperature T, the folowing condition must hold:
p_ne^(e_n/kT)Bⁿ_mr) = p_me^(e_m/kT)(B^m_mr + Aⁿ_m)
From this equilibrium condition and Wien's displacement law, Einstein then derived Planck's radiation law, as well as Bohr's frequency condition:
e_n - e_m
The terms A, B are known as the Einstein coefficients. They were used in Dr. Charles H. Townes' theory of the microwave maser, representing the rate at which an electron makes a transition due to spontaneous emission or stimulated emission. From this, the laser was developed.
In Introduction to Theory and Applications of Quantum Mechanics (1968), Amon Yariv gives a derivation of this which (implicitly) sets forth the antitonic nature of this process. In the emission process, an atom goes to a lower energy state (MINTONE) while the radiation mode increases a step (MAXTONE).