15_lecnotes_rwf

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

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

View Full Document Right Arrow Icon
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 d 2 A = 1 2 [ [ A H H ] ] , , i 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 1 k 11 33 1 2 3 2 , a a k 1 22 1 2 2 , a a H ( ) = ( ΩΩ + ΩΩ 1 ) + ( ΩΩ + ΩΩ 2 ) 1 2
Image of page 1

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

View Full Document Right Arrow Icon
5.74 RWF Lecture #15 15 – 2 The Two-Level Problem Again E 0 δ E 0 H = + + Ω + Ω 0 E 0 −δ E E = E A + E B δ E = E A E B 2 2 0 0 Ω = 0 V ΩΩ = Ω = 0 0 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 θ 2 e iE t ( ) Ψ 0 = cos + − sin θ in the +,– basis and 2 e iE + t ( cos ( ) Ψ t = cos θ 2 θ A + sin θ 2 B ) sin θ 2 e iE t ( sin θ 2 A + cos θ 2 B ) 2 θ 2 e iE + t θ 2 e iE t = ( cos + sin 2 A iE + t iE t ) θ ) + cos 2sin θ 2 ( e
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern