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Unformatted text preview: Supplementary Notes for Week 3 and 4 Changyi Li January 31, 2010 Selection Rules As shown in the Einstein Coe cient section of week 2's supplementary notes, the transition probability is given by the Fermi's Golden Rule, P = 2 π ~ h f  V  i i 2 ρ (1) where f is the nal state and i is the initial state. ρ is the density of states for the nal state and V is the perturbation to the original Hamiltonians of the system. In the case shown in week 2, V =→ μ ·→ E , therefore P ∝ h f → μ  i i 2 (2) or the transition dipole moment squared. In other words, if our transition dipole integral turns out to be 0, we will have 0 probability of such a transition, or forbidden by symmetry. The rules by which we determine which transitions are allowed are called the selection rules. The selection rules for rudimentary systems such as particleinabox, harmonic potential, anharmonic potential with cubic and quartic anharmonicity, hydrogenlike atom are listed in the lecture slides. Due to the importance of the carbonyl bond, formaldehyde is used as an example in the lecture slide and the π → π * transition is used as an example. In case one example is not su cient, here I will show (with help from Sunney's omitted slides) how the selection rules apply to the n → π * transition. The problem start out the same way: determine the planes of symmetry of the C=O bond, for which there are 2: the xy plane and the xz plane. σ signi es a symmetry operation called re ection , which is to re ect the molecule with respect to the plane. For example, for the operationre ect the molecule with respect to the plane....
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This note was uploaded on 10/27/2010 for the course BI 110 taught by Professor Richards,j during the Winter '08 term at Caltech.
 Winter '08
 Richards,J

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