DOC PREVIEW
MIT 5 74 - Absorption Lineshape for the Displaced Harmonic Oscillator Model

This preview shows page 1 out of 4 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 4 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 4 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

MIT OpenCourseWarehttp://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.δ g() Absorption Lineshape for the Displaced Harmonic Oscillator Model Finite temperature calculations Lets work in units of k := 1 hbar := 1 Define the frequency of the electronic transition:Ω0 := 10 ωeg := Ω0 and the vibrational frequency: ω0 := 1 The unitless displacement of the two harmonic wells is: D := 0.5 − 1 ⋅Define thermal occupation factor nT := ⎜⎛ exp ⎛ hbar ω0 ⎟⎞ ⎞( ) ⎜− 1⎟ ⋅ := if g = 0 , 1 , 0 ⎝ ⎝ kT⎠ ⎠ ( ) Set up frequency grid: i := 0 .. 100 ωi := −5 + Ω0 + 0.1 i⋅ Absorption lineshape: JK− D⋅(2n T⋅ ()+1)10 10 ⎡D+ J K ⎤ σω, T ) := π⋅e ⋅⋅( () + 1) ⋅ ()⋅ δω− ω − (J − K( ∑ ∑ ⎣⎢ J!⋅K! nT nT⎣⎡ ⎣⎡ eg )⋅ω0⎦⎤⎦⎤⎦⎥ J = 0 K = 0 Envelope of vibronic progression: π ⎡⎢ −(ω− ωeg − D⋅ω0)2 ⎤⎥Env(ω, T) := ⎡ 2 ⎤⋅exp⎢ 2 ⎥ ⎣D⋅ω0 ⋅( ⋅ () + 1)⎦ ⎣ ⋅⋅ω0 ⋅( ⋅⎦2nT2D () + 1)2nTPlot lineshapes for low, mid and high temperatures. Temperature is defined relative to nuclear frequency (T/ω) ω0 a T = ∞() := 0.01 T 3 σω( i , T) 2 Env(ωi , T)1 0− 6 − 4 − 2 0 2 4 6 ωi−ωeg ω0b T := 1 = 1() T 2 1.5 σωi , T( ) 1 Env(ωi , T) 0.5 0− 6 − 4 − 2 0 2 4 6 ωi−ωeg ω0 c T := 3 = 0.333() T 1.5 σω( i , T) 1 Env(ωi , T) 0.5 0− 6 − 4 − 2 0 2 4 6 ωi−ωeg2− 1− 0 1 σωi 2,( ) σωi 1,( )1−σωi 0.01,( )2−ω0 T 0.333= ω0 T 1= ω0 T ∞= D = 0.5 ω0 = 1 − 4 − 2 0 2 4 6


View Full Document
Download Absorption Lineshape for the Displaced Harmonic Oscillator Model
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Absorption Lineshape for the Displaced Harmonic Oscillator Model and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Absorption Lineshape for the Displaced Harmonic Oscillator Model 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?