07_lecnotes_rwf

07_lecnotes_rwf - MIT Department of Chemistry 5.74 Spring...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
5.74 RWF Lecture #7 7 – 1 Motion of Center of Wavepacket Last time: Discussed experiments to monitor the central quantity ⟨Ψ( t )|Ψ(0)⟩ in Heller’s picture: the absorption spectrum, I ( ω ), is the FT of the autocorrelation function. Ψ (0) in the autocorrelation function is the ground state, ′′ VR g (), vibrational wavefunction gv g , transferred vertically onto the excited state potential, e (). Is there a way to monitor ⟨Ψ( t )|Ψ(0)⟩ directly in the time domain? Many suggested schemes. We need tools to examine various excitation/detection experimental schemes. Excitation at t = 0, E (0) Evolution, U ( t ,0) = e –i H t/ h Detection, D ρ ( t ) = U ( t ,0) E (0) ρ (0) E (0) U ( t ,0) Observation: Trace ( D ρ ( t )) Consider the simplest 3 level system first 2 1 0 MIT Department of Chemistry 5.74, Spring 2004: Introductory Quantum Mechanics II Instructor: Prof. Robert Field
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
5.74 RWF Lecture #7 7 – 2 Short excitation pulse Ψ () // / te e e iE t iE t iE t =+ + −− βα α 012 01 2 12 hh h both eigenstates |1 and |2 are bright β = [1 – | α 1 | 2 + | α 2 | 2 ] 1/2 α i = c i μ i 0 c i describes the intensity, spectral distribution, phase, and duration of the excitation pulse. μ i0 is the electric dipole transition moment ρρ ** t ee it == +− ++ ΨΨ ββ α β α α αα α ωω 2 11 2 21 2 2 2 01 02 01 12 02 12 This ρ ( t ) is obtained by two transformations of ρ (0) ρ ( t ) = U ( t ,0)
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 7

07_lecnotes_rwf - MIT Department of Chemistry 5.74 Spring...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online