13_lecnotes_rwf

13_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 #13 13 – 1 Polyads, a, a , N Readings : Chapter 9.4.4 - 9.4.9, The Spectra and Dynamics of Diatomic Molecules , H. Lefebvre-Brion and R. Field, 2 nd Ed., Academic Press, 2004. Last time: ( ) two level problem with complex E j 0 . strong coupling limit V 2 >> δε 2 + δΓ 2 /4 : if either δε = 0 or δΓ = 0, the two quasi-eigenstates have the same width. Otherwise no major surprises. weak coupling limit V 2 << δε 2 δΓ 2 /4 : if δε = 0 we get no level repulsion and no level-width sharing. Big surprise! Quantum beats between two decaying quasi-eigenstates. I( t ) expressed in terms of 8 parameters (I + , I , Γ + , Γ , I QB , Γ QB , ω QB , φ QB ) obtained from 6 dynamical parameters ( δε , δΓ , Γ , V , I A , I B ). H Today: begin study of vibrational dynamics, leading eventually to replacement of the quantum mechanical± eff by a classical mechanical H eff . Tricks to get A without use of Trace( Αρ ( t )).± Polyatomic Molecule Vibration 3 N = ψ V = φ v j product basis set± 1 2 v ψ v v 3 N 6 j = 1 3 N H = h j + coupling terms± j = 1 243 4 H ( ) 0 could also include diagonal anharmonicities 0 / E ( ) = h ω j ( v j + 1 2 ) (traditionally ω is in cm –1 units, E = hc ω ( v + 1/2), and ω is not in j radians/s) coupling terms have the form k ijk Q Q Q + { quartic } + { quintic } +… i j i j k ± , , cubic most important Enormous number of undeterminable anharmonic force constant terms.
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 #13 13 – 2 matrix element scaling and selection rules a scaling = 2 π c µ ω j a /2 { v a j highest power term /2 } (and similarly for P a j ) v j + n v j Q selection rule n = a , a – 2, … – a µ and ω j must be generalized from single oscillator (diatomic molecule) form via a Wilson force constant geometry F , G matrix j
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