Sound amplification by stimulated emission of radiation frequencies ) of the phonons as a function of their wave vector's "k" . The relationship between frequency "ω" and wave vector "k" is called phonon dispersion. Light and sound are similar in various ways. They both can be thought of in terms of waves, and they both come in quantum mechanical units. In the case of light we have photons while in sound we have phonons. Both sound and light can be produced as random collections of quanta (e.g. light emitted by a light bulb) or orderly waves that travel in a coordinated form (e.g. laser light). This parallelism
Stimulated emission given by where the proportionality constant "B" is known as the "Einstein B coefficient" for that particular transition, and "ρ"("ν") is the radiation density of the incident field at frequency "ν". The rate of emission is thus proportional to the number of atoms in the excited state "N", and to the density of incident photons. At the same time, there will be a process of atomic absorption which "removes" energy from the field while raising electrons from the lower state to the upper state. Its rate is given by an essentially identical equation, The rate of absorption is thus proportional