MIT5_74s09_pset04

MIT5_74s09_pset04 - MIT OpenCourseWare http:/ocw.mit.edu...

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MIT OpenCourseWare http://ocw.mit.edu 5.74 Introductory Quantum Mechanics II Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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5.74, Problem Set #4 Spring 2009 Due Date: Mar. 19, 2009 1. Displaced Harmonic Oscillator Model at Finite Temperature Based on the correlation function for the position of the harmonic oscillator that you derived in the last problem set, it should be apparent that the energy gap correlation function eg () for Ct coupling to a single harmonic mode is written 2 −ω δω eg t δω eg ( 0 ) = ω 0 D ( n + 1 ) e it 0 + n e i 0 t Here n is the thermally averaged occupation of the harmonic oscillator. a) Using , find the real and imaginary parts of the lineshape function gt () = g ( t ) + i g ′′ ( t ) . eg 22 b) Calculate the absorption lineshape using the short time expansion e 0 1 i 0 t 0 t ≈−ω 2 . What is the linewidth and how does it scale with temperature for kT >> ω 0 ? h 2. Absorption lineshape from a frequency correlation function.
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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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MIT5_74s09_pset04 - MIT OpenCourseWare http:/ocw.mit.edu...

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