15_lecnotes_rwf

15_lecnotes_rwf - MIT Department of Chemistry 5.74, Spring...

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MIT Department of Chemistry 5.74, Spring 2004: Introductory Quantum Mechanics II Instructor: Prof. Robert Field 5.74 RWF Lecture #15 15 – 1 Visualizing IVR . [ Chem. Phys. Lett. 320, 553 (2000)] Readings : Chapter 9.4.9 and 9.4.10, The Spectra and Dynamics of Diatomic Molecules , H. Lefebvre- Brion and R. Field, 2 nd Ed., Academic Press, 2004. Last time: Looking for causes of dynamics d A = [ A H ] , dt i h d 2 A = 1 2 [ [ A H H ] ] ,, i h dt 2 discussed 3 mode, 2 resonance model (H 2 O)± derived many operator relationships for ⟨Ν d Ν ⟩ is transfer rate operators± Ν j found that the cause of dt ⟨Ν j # of quanta changed d 2 e.g. N = ΩΩ 2 − ΩΩ 2 dt i h 1 k 11 33 1 2 3 2 , aa k 122 12 2 , H () = (ΩΩ + ΩΩ 1 ) + (ΩΩ + ΩΩ 2 ) 1 2
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5.74 RWF Lecture #15 15 – 2 The Two-Level Problem Again E 0 δ E 0 H = + + Ω + Ω ΩΩ 0 E 0 −δ E E = E A + E B δ E = E A E B 2 2 0 0 Ω= 0 V = Ω = 00 V * 0 We are going to let V be real Suppose our pluck at t = 0 is ψ A Ψ (0) = A = cos θ /2 + – sin θ /2 verify by plugging in += cos θ 2 A + sin θ 2 B −=− sin θ 2 A + cos θ 2 B 2 () Ψ 0 = cos θ 2 A + cos θ 2sin 2 B + sin 2 2 A cos 2sin 2 B 2 = ( cos θ 2 + sin 2 θ 2 ) A . θ θ θ θ checks Now put in t -dependence: 2 e iE + t h θ 2 e iE t h Ψ 0 = cos + − sin θ in the +,– basis and 2 e iE + t h ( cos Ψ t = cos θ 2 θ A + sin θ 2 B ) sin θ 2 e iE t h (− sin θ 2 A + cos θ 2 B ) 2 θ 2 e iE + t h θ 2 e iE t h = ( cos + sin 2 A iE + t h iE t h ) θ ) + cos 2sin
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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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15_lecnotes_rwf - MIT Department of Chemistry 5.74, Spring...

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