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In the classical description of the Raman effect the object of study is the electric polarizability of the system. I'm interested in learning the quantum description of the Raman effect and in Bernath's "Spectra of atoms and molecules" it is said that we are interested in studying the transition dipole moment like: \begin{equation} M_{10}=\langle {\Psi_1\mid}\mu{\mid\Psi_0}\rangle \end{equation} Where $\mid\Psi_i\rangle$ are the $i-$level state of the system.

How are these two descriptions related?

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    $\begingroup$ The formula that you give is valid for electronic transition between states 0 and 1 but not for Raman scattering, where no second state is involved. Quantum mechanical description of Raman scattering is quite complicated, you can start here if you are interested: www2.fkf.mpg.de/keimer/lecture/Solid_State_Spect_2014/… $\endgroup$
    – gigacyan
    Commented Aug 21, 2014 at 7:24
  • $\begingroup$ @gigacyan The link you've given requires authentication... It appears here though, however still requiring signing in.... fkf.mpg.de/1786169/Teaching $\endgroup$
    – Cheng
    Commented Jan 7, 2023 at 11:01

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The Raman effect is a Quantum effect in nature which proves the Photon nature of Visible light. Suppose an intense beam of blue light is passed through a material consisting of molecules; then a very weak portion of the scattered light changes in wavelength and thus in colour. What happens is the light which is passing just has same energy and wavelength but when scattered it generates light beams of different colours or wavelength. Part of energy of the Photons is transferred to the molecules and the rest is scattered.

The Quantum law was Discovered by A. Smekal, according to which $E + h\nu=E' + h\nu'$.

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