University:
Widener University
Course:
PHYS-121 | Fundamentals of Physics I
Academic year:

2023
Views:

354

Pages:

4
Author:

sneeublom897

Page 1 of 4 pages Lecture #35: Finish Wavepacket Dynamics I(ω) = ∫ ∞ −∞ e−iωt ψ(t) ψ(0) dt pictures of ψ(t) ψ(0) absorption spectrum is | ″〉 propagating on V′(R). This is a superposition of several v′j Ψ(t) ψ(0) 2 t What is FT of sin ωt? I(ω) ω Page 2 of 4 pages What is FT of I(ω) ω 2ω 3ω odd harmonics only What is FT of exponen t OR What is FT of ψ(t) ψ(0) τ |← T 1 T= ωec 2τ →| for HO t 1 2τ I(ω) ω location of vertical transition Page 3 of 4 pages Classical Period Initial decay, duration of recurrence peaks. F =− dV = mR dR R′(0) = R′< = R′′e dR′(t = 0) =0 dt 1 dV ′ ( Re′′) R ′(t ) = − t m dR ⎛ 1 dV ′ ( Re′′) ⎞ 2 R′(t ) = Re′′ + ⎜ − ⎟t ⎝ m dR ⎠ Ignore the curvature of V(R) How long does it take for R′(t) − R′′e = ² (the width of the initial wavepacket)? ⎡ m² ⎤ τ ≈⎢ ⎣ −dV / dR ⎥⎦ 1/ 2 How is dV related to ω? dR V(R) = 1 2 k (R − R e ) 2 dV = k (R − R e ) = µω2 (R − R e ) dR dV′ (R′′e ) = µω′e2 (R′′e − R′e ) dR 1/ 2 m2 ⎛ ⎞ τ∝⎜ 2 ⎝ µ ω′e ( Re′′ − Re′ ) ⎟⎠ Does ∆ depend on ω′′e ? Page 4 of 4 pages E= 1 1 2 ωe hc = k ( R − Re ) 2 2 ( 2 / 2 )2 ωe hc = k ( 2 / 2 ) 1 2ωe 2 ⎛ ωe ⎞ ⎜ 4 hc ⎟ ⎝ k ⎠ 1/ 2 ⎛ 4hc ⎞ ⎜ 1/ 2 ⎟ ⎝ (kµ) ⎠ =² ω2m 1/ 2 ⎛ 4hc ⎞ ⎜ ⎟ ⎝ ωµ ⎠ =² 1/ 2 τ ≈ α ω′e a constant −1.25 =² (R′′e − R′e ) −1/2