16_lecnotes_rwf - MIT Department of Chemistry 5.74, Spring...

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MIT Department of Chemistry 5.74, Spring 2004: Introductory Quantum Mechanics II Instructor: Prof. Robert Field 5.74 RWF Lecture #16 16 – 1 Normal Local Modes: Classical, Morse, Minimal Model Reading : Chapter 9.4.12, The Spectra and Dynamics of Diatomic Molecules , H. Lefebvre-Brion and R. Field, 2 nd Ed., Academic Press, 2004. Last time: two level problem (A,B), (+,–) Ψ (0) = A ρ ( t ) in (A,B) and (+,–) representations H = H diag + H res H diag () = E diag t res = t H = ΩΩ k + ΩΩ k E res κ E = E diag + E t t res E res, j = lim 1 T dt ( ΩΩ + ΩΩ j ) T →∞ T 0 j E res, j f j = E res
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5.74 RWF Lecture #16 16 – 2 Today: Preparation for exam Correction of misconceptions from Lecture #15 Overtone Spectroscopy Classical treatment of 2 coupled harmonic oscillations Consider excitation of a molecule, like H 2 O, with two short pulses of radiation. The two pulses have different center frequencies and the second pulse can be delayed by τ relative to the first pulse, for 0 ≤ τ ≤ 10 ps . After the two pulses have exited the sample, populations in the two-step excited eigenstates are measured by an unspecified method. The measured quantity is ρ ff ( τ ) for each of the eigenstates in the two-step excited polyad (see figure) on page 16-3. At t = 0 prepare Ψ (0) = A ** Only µ aA and µ bB (basis state to basis state) transition moments are non-zero. The population in each of the two-step excited eigenstates, ρ ff ( τ ), as a function of delay between the two pulses is ρ ( τ ) () = Ψ () Ψ ρτ f δµµ τ τ δµµ f ff
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This note was uploaded on 11/28/2011 for the course CHEM 5.74 taught by Professor Robertfield during the Spring '04 term at MIT.

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16_lecnotes_rwf - MIT Department of Chemistry 5.74, Spring...

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