10supp_lec_rwf

10supp_lec_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 #10 Supplement 10S – 1 Stationary Phase for Vibration-Electronic Spectra Consider two electronic potential energy curves R V (R) V (R) T e E vib ′′ E vib R e R e E The classical Franck-Condon principle specifies R = 0, P = 0. If P = 0, then the kinetic energy, KE( R ), must also be unchanged upon excitation R KE () = E V R vib R KE = E ′′ − V R vib thus E E ′′ = V V R R vib vib which can only be satisfied at special values of R, each of which is a stationary phase point. The choice of transition frequency from a given vibrational level of either the lower or upper electronic state determines the stationary phase point. This is the R -value (or R -values) at which the transition occurs and the region where a piece of the initial state wavefunction is transferred onto the final state potential.
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5.74 RWF Lecture #10 Supplement 10S – 2 The transition frequency h ν=∆ T e + E E ′′ =∆ T e + V () V ′′ R R vib vib h ν R R −∆ T e = V V = V ( R s p ) V ( R s p ) specified by the experimentalist satisfied at R sp R sp may be swept through a small region of the initial state vibrational wavefunction by systematic variation of the center frequency of the probe laser, ν . As R sp sweeps through lobes of the initial state wavefunction, the transition amplitude increases and decreases. The maximum transition amplitude is obtained when
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10supp_lec_rwf - MIT Department of Chemistry 5.74 Spring...

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