08_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 #8 8 – 1 Resonance Operators: Equation of Motion Last time: tools for describing a pump/probe wavepacket experiment * ρ ( t 0) incoherent, populations on diagonal * E (0) excitation matrix. Transforms initial state into coherent superposition: for electronic transition get gv g ′′ , translated vertically onto upper potential surface * U ( t ,0) = e –i H t/ h time evolution of t = 0 prepared wavepacket. If ρ (0) = E (0) ρ ( t 0) E is expressed in the eigenbasis, U has simple diagonal form. Otherwise need to express everything in zero- order basis and transform.± Why? The pluck is almost always a simple zero-order non-eigenstate.± ρ (t) = U ( t ,0) E (0) ρ ( t 0) E (0) U ( t ,0) * Now describe the specific nature of the detection operation I( t ) = Trace( D ρ ) If you want to sample the ρ ij ( t ) element of ρ ( t ), you want a detection matrix with non-zero D ji element. Often we observe something in an experiment like aa ii Q , P i i P i 2 m V 2 t Ψ () Ψ and we would like to understand what this implies about the dynamical mechanism where does it start? how fast does it leave? why? where does it go next? why? how fast does it go there? why? what fraction gets to the target state? why? We build a toy model H eff with the goal of reproducing the early time dynamics. We want to be able to look at the toy model and identify the most important dynamical features of that model. dynamical feature model parameter, dynamical mechanism Tools for computing dynamics from H model ! or constructing H model from expt.
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5.74 RWF Lecture #8 8 – 2 Today: useful ways of monitoring and describing the mechanism of the dynamics encoded in ρ ( t ).
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08_lecnotes_rwf - MIT Department of Chemistry 5.74 Spring...

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