Polarizability if a molecule in raman scattering

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SUMMARY

The discussion focuses on the polarizability of a molecule in Raman scattering, specifically how it scales with the quantum number v for anti-Stokes transitions and v+1 for Stokes transitions. The derivation relies on the harmonic oscillator model, where matrix elements are expressed as \langle v|x,y,z|v\pm 1\rangle \langle v\pm 1 | x,y,z |v\rangle. Understanding this relationship requires familiarity with quantum mechanics and the use of creation and annihilation operators.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Understanding of harmonic oscillators
  • Familiarity with Raman scattering principles
  • Knowledge of matrix elements in quantum mechanics
NEXT STEPS
  • Study the derivation of polarizability in Raman scattering
  • Learn about the role of creation and annihilation operators in quantum mechanics
  • Explore the differences between Stokes and anti-Stokes transitions
  • Review harmonic oscillator models in quantum mechanics
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Students and researchers in physical chemistry, quantum mechanics enthusiasts, and professionals studying molecular spectroscopy and Raman scattering techniques.

Mr Boom
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Hello. I'm reviewing background information on Raman scattering and I've noticed that the polarizability scales with v+1 for Stokes transitions and v for anti-Stokes. Why is this and what assumptions are used in the derivation? An explanation or pointing me to a good reference would be appreciated.

Thanks
 
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I don't understand your question- what is 'v'?
 
I think v is the quantum number n of the oscillator involved.
I can only give you a scetch:
In Raman scattering you have matrix elements \langle v|x,y,z|v\pm 1\rangle \langle v\pm 1 | x,y,z |v\rangle. If the vibrations are harmonic these expressions scale like v or v+1. Try to express x, y or z in terms of generation and anihilation operators b+ and b to prove this.
 

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