Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 197

Substituting the radiation density into (S.4.80.4) gives

or

The ratios of coefficients may be found by considering (S.4.80.6) for extreme

values of since it must be true for all values of For very large values of

we have

Substituting (S.4.80.7) back into (S.4.80.6) yields

or

which immediately yields

and so, from (S.4.80.7),

c) Inspection of (S.4.80.11) shows that the ratio of the spontaneous emission

rate to the stimulated emission rate grows as the cube of the frequency,

which makes it more difficult to create the population inversion necessary

for laser action. The pump power would therefore scale as

4.81 Atomic Paramagnetism (Rutgers, Boston)

a) The energy associated with the magnetic field is

where is an integer varying in the range