# Quantum Theory of Raman Effect

## Quantum Theory of Raman Effect

Quantum theory of the Raman effect explains the phenomenon by considering the interaction between incident photons and vibrational modes of molecules of the system.It imagines perfectly elastic collisions taking place between the light photons with energy h𝜈 and molecules of mass m in energy state E

_{p}moving with a velocity v. After collision, if E

_{q}is the energy state of the molecule and v' is its velocity then-

E

_{p}+ ½ mv

^{2}+ h𝜈 = E

_{q}+ ½ mv'

^{2}+ h𝜈'

where, v and v' are the velocities of photon before and after collision respectively.

It can be easily proved that the velocity of the molecule practically remain unchanged.

we have-

E

_{p}+ h𝜈 = E

_{q}+ h𝜈'

or, v' = v + [E

_{p}− E

_{q}]/h

or, v' = v + Δv

From this equation, we have three cases-

**Case-1:**

If E

_{p}= E

_{q}, then Δv = 0

Thus, in such collision the molecule simply deflects the photon so it is analogous to Rayleing scattering.

**Case-2:**

If E

_{p}> E

_{q}, then v' > v

This correspond to Anti-Stokes' lines.

Thus, in this case, molecule transfers some of its energy to the photon.

**Case-3:**

If E

_{p}< E

_{q}, then v' < v

This correspond to Stokes' lines.

Thus, in this case, molecule absorbs some of its energy to the photon.