1. Scattering: Raman and Rayleigh 0 s i,f 0 s 0 s i Rayleigh Stokes Raman Anti-Stokes Raman i f f nnn http://www.doitpoms.ac.uk/tlplib/raman/raman_microspectroscopy.php Two photons/simultaneous

2. E0E0 EsEs

4. Kramers-Heisenberg-Dirac Equation  a damping factor to avoid infinity at resonance

5. Kramers-Heisenberg-Dirac Equation  a damping factor to avoid infinity at resonance

6. Derivation using 1 st -order Time-dependent perturbation theory The field must perturb the zero order wavefunction in order to induce a transition dipole moment

7. Apply the perturbation field to both states i and f.

8. Evaluate using same procedure developed before insert trial wavefunction into perturbed Hamiltonian Multiply through by a basis function Solve for dc n /dt and integrate to get each time- dependent c Keep all c’s And similarly for i

9. The function V has the form:

10. With these c’s can write the wavefunction

11. Our interest is in induced moments that follow the applied field, not the fixed frequency  nf component. The “rotating wave approximation”

12. Evaluating this with the wavefunction we just derived: The leading terms in the zero order states give.

13. The cross terms of zero order states with first-order corrected states gives (neglect square of corrected states): Expand V nf

14.  if Define a phenomenological damping to avoid infinity on resonance, usually derived from expt.

15.  if Define a phenomenological damping to avoid infinity on resonance, usually derived from expt. “resonance term”

16. EsEs

17. Monday: Rotational Spectroscopy CH8