{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MIT5_74s09_pset04

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

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

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 .

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

View Full Document
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.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

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

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

View Full Document
Ask a homework question - tutors are online