#### Light -Atom Interaction - Part 4

 In this part      1. we evaluate the details of the light emission rates      2. discuss the stimulated emission      3. shortly mention the laser      4. shortly discuss the physics of molecules - and their spectra The notation here should be now clear: Golden Rule, Probability change rate W, density of states The interaction HI  has been discussed - comes basicaly from the Lorentz Force 010_Golden_Rule.png        010_Golden_Rule.png The momentum operator p is the momentum of the electron; A is the operator of the "vector potential" of the field And thus expressed using the mode's creation, anihilation operators Note that we must be summing over "all the modes";  e the polarization vector Initial and final states are mentioned - here generally   -  see below for a more specific discussion Note that there is also a definition of the "transition frequency" in terms of energies 020_Golden_Rule_Applied.png        020_Golden_Rule_Applied.png Next slide - everything is inserted - the constant expressing the field dimensions (square root....),  density of states etc 030_Golden_Rule_Applied_details.png        030_Golden_Rule_Applied_details.png Here are the details of the matrix element evaluation    what are electronic (red) and what are field (blue) components    As mentioned before, the field is quantized, its description is in terms of creation/anihilation expressions             but the "eigenmodes" are in the normal 3-dim space - so they will be the same as the electron coordinates                                                                            (   the exp(i k r ) - r is the same coordinate as the electron )                                             Also note the problem    exp(i k r - i omega t )    and exp( - i k r + i omega t ) - seems to be                                                                            inconsistent conventions   - we do not have the solution yet 040_Matrix_Element_details.png        040_Matrix_Element_details.png Further simplifications  - so called Dipole approximation                   first  -  long wavelength approximation, get rid of the exponential exp ( i k r )                   then transform the p-operator matrix element  to the matrix element of r - that makes the dipole 050_dipole_approximation.png        050_dipole_approximation.png More on Dipole approximation                    transforming the p-operator matrix element  to the matrix element of r - that makes the dipole                    using the commutation relation  [ r, H ] 060_dipole_approximation.png        060_dipole_approximation.png Working with the "density of states "    when discussing that - we left the integration over the directions open        now we shall perform the integration over directions        This is somewhat too detailed, discussed only for completeness        This is done in a clever way:   the  < b |   p  |  a   >    is a given vector (three numers, while vector p is 3 operators )                                                        Thus this vector is chosen as a definition of the z-axis, very clever!                                                        Mentioned at the end of this slide, used in next slide 070_evaluation_details_emission_angle.png        070_evaluation_details_emission_angle.png Working with the "density of states "      - performing the integration over directions              (   This is somewhat too detailed, discussed only for completeness   )        This is done in a clever way:   the  < b |   p  |  a   > = P'   is a given vector (three numers, while vector p is 3 operators )                                                        Thus this vector is chosen as a definition of the z-axis, very clever!         This also includes summation over the polarizations  -  even more clever trick - with this choice of axes                                                                                       only one polarization   ( but in "real space" no such exclusion! )                                         ( look at the rounded frames ..... the 0 scalar product) 080_evaluation_details_emission_angle.png        080_evaluation_details_emission_angle.png Now this is combined into the expressions from before, look at the simple integral giving the 8 pi/3 result 090_evaluation_details_emission_angle.png        090_evaluation_details_emission_angle.png ---- 100_Final_result_Physics_dimensions.png        100_Final_result_Physics_dimensions.png Understanding stimulated emission in the language of creation/anihilation operators      This is really one of the nicest results here 110_stimulated_emission.png        110_stimulated_emission.png The story of the LASER  - a popular presentation - this explains "Population Inversion" 180_population_inversion.png        180_population_inversion.png The laser light is ( ideally ) much more a "classical wave" than "stream of photons"  Nobel prize winner Roy Glauber ( just turned 90 this november, congratulations! ) explained this  Glauber states       http://folk.uib.no/nfylk/PHYSTOYS/glauber/ 190_coherent_states_H.O.png        190_coherent_states_H.O.png The basics of Molecular physics      Why are molecules bound states    -  electronic states   - H2+   example  (hydrogen molecule ion ) 250_Molecular_Binding_Spectra_etc.png        250_Molecular_Binding_Spectra_etc.png Electronic states in a homonuclear molecule (bothe nuclei the same, homogeneous ... ) 290_molecular_binding.png        290_molecular_binding.png Three types of molecular spectra         - electronic states    (  ~  eV )         - vibrational states   (  ~ 0.01  eV )         - vibrational states   (  ~  0.001 eV ) 300_molecular-spectra_elctr_vibr_rot.png        300_molecular-spectra_elctr_vibr_rot.png It might be of interest to look at older notes, for example       http://web.ift.uib.no/AMOS/PHYS261/2011_11_10/                    where we have listed also even older links                    Molecules                      http://web.ift.uib.no/AMOS/PHYS261/03.11.12/index0.html                    Exotic Atoms                      http://web.ift.uib.no/AMOS/PHYS261/2004.11.18/index0.html                      2004.10.07 Blackboard shots; Molecular Physics                                                  Pictures of molecular states                       2004.10.27 Blackboard shots; Last part Molecular Physics                    Lecture: Physics of Molecules                       2004.11.17 Short blackboard shots; Effects, Structures Spectra. Dirac equation                       2004.11.18 Blackboard shots; Effects, Structures Spectra. Exotic and Hollow Atoms