17_lecnotes_rwf

17_lecnotes_rwf - MIT Department of Chemistry 5.74 Spring...

Info icon This preview shows pages 1–4. 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 #17 17 – 1 Normal Local Modes: 6-Parameter Models Reading : Chapter 9.4.12.5, The Spectra and Dynamics of Diatomic Molecules , H. Lefebvre-Brion and R. Field, 2 nd Ed., Academic Press, 2004. Last time: ω 1 , τ, ω 2 (measure populations) experiment ω 2 ω 1 ( abcd ) ( AB ) g two polyads.± populations in (1234) depend on τ E res, k could use f k = to devise optimal plucks for more complex situations± E res± (choice of plucks and probes)± * multiple resonances * more than 2 levels in polyad Overtone Spectroscopy± nRH single resonance± nRH + 1RH double resonance± dynamics in frequency domain± Today: Classical Mechanics: 2 1 : 1 coupled local harmonic oscillators± QM: Morse oscillator± 2 Anharmonically Coupled Local Morse Oscillators± eff . Antagonism. Local vs. Normal. H Local Whenever you have two identical subsystems, energy will flow rapidly between them unless something special makes them dynamically different: * anharmonicity * interaction with surroundings± spontaneous symmetry - breaking± eff Next time: H Normal .
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 #17 17 – 2 Two coupled identical harmonic oscillators: Classical Mechanics H T = ( ) P P R L , V + ( ) Q Q R L , ( ) R = Right, L = Left T = ( ) P P P P R L R L , 1 2 G geometry and masses 1 rr ( R 2 + P L 2 ) + 2 G P P = [ G P rr R L ] R L ) F Q R V = ( Q Q Q 2 L force constants 1 2 rr ( R + Q 2 ) + 2 F Q R Q = [ F Q L rr L ] 2 rr R rr L + 2 2 2 2 ( ) 0 ( ) rr R rr L F Q F Q 2 H = 1 G P 2 + 1 2 1 G P 2 + 1 H R 0 H L rr R L + F Q Q + G P P rr R L kinetic potential (anharmonic) coupling coupling
Image of page 2
3 5.74 RWF Lecture #17 17 – 3 φ 2 1 1 1 1 + m 1 3 m G rr = + = + = = F rr k = µ m 1 m 2 m m m 3 m 3 1 3 F rr 1 k RL cos φ (projection of velocity of for stretch onto = G rr = m 3 direction) kinetic coupling gets small for large m or φ = π /2 Each harmonic oscillator has a natural frequency, ω 0 : 1 2 / 1 F G rr rr ] 1 2 / = π µ [ π c ω = and the coupling is via 1 : 1 kinetic energy and potential energy coupling terms.
Image of page 3

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

View Full Document Right Arrow Icon
Image of page 4
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