A GENERALIZED LANGEVIN EQUATION FOR WAVE-FUNCTIONS - INTRAMOLECULAR VIBRATIONAL DEPHASING AS A STOCHASTIC-PROCESS

A generalized Langevin equation satisfied by time-evolving wave functi ons is derived by adapting the Mori formalism to the Schrodinger time dependent equation. The equation obtained describes both deterministic and stochastic time evolution of wave functions. Memory kernel of the ''delayed friction'' term of the equation obtained consists of the te mporal correlation function (in the quantum mechanical sense) among no n-stationary wave functions, i.e., wave packets. The memory is likely to decline rapidly essentially due to the dispersion of the wave packe ts, so that a ''Markov'' limit is justified. An ensemble of probabilit y amplitudes of different quantum states is considered, and the probab ility distribution of these probability amplitudes is discussed. This probability distribution is connected with spectroscopic observables: It can be derived from excitation profiles of Raman scattering amplitu des with many different final states. By assuming the ''random force'' term of the Langevin equation to be Gaussian white noise, a Fokker-Pl anck equation is derived. The solution of this Fokker-Planck equation describes how ''randomization'' proceeds in intramolecular vibrational dephasing. As time goes to infinity, all the accessible states are eq ually populated on the average, but fluctuation around the ''microcano nical equilibrium'' remains.