Energy Gaussian wave packets

Figure 4. Diabatic (solid lines) and adiabatic (dashed lines) potential-energy curves of Model IVa. The Gaussian wave packet indicates the initial preparation of the system at time t = 0.

The subspace of positive energies does not contain strictly localized spinors. There is no wave function that vanishes everywhere in an open region of space. All positive-energy wave packets are essentially spread over all of space. Still, there are wave packets which are approximately localized in the same sense as a Gaussian wave packet, i.e., they vanish faster than any inverse power of x, as x goes to infinity. Examples of such Gaussian-type wave packets are in Figures 3 and 4. 

Figure 7 The time auto correlation function and the corresponding spectrum for a Gaussian wave packet propagating on an excited harmonic potential energy surface, (a) The short time decay of C(/) (cf. Eq. (17)) and the broad spectrum (= the Franck Condon envelope (cf. (18)). (b)The longer time dependence of C(r) and the corresponding, vibrationally resolved, spectrum.

Habershon S (2012) Linear dependence and energy conservation in Gaussian wave packet basis sets. J Chem Phys 136 014109... 

Ohrn and co-workers have developed a direct dynamics approach which incorporates both the electrons and nuclei dynamics (END).""" The complete electron-nuclear coupling terms are retained in the calculation and, as a result, the dynamics is not constrained to a single Born-Oppenheimer potential energy surface i.e., electronic non-adiabaticity is explicitly included. A complication in this approach is the computational demand in propagating an electronic wavefunction which is an accurate representation of the ground electronic state as well as multiple excited electronic states. This approach will become more widely used as computation becomes more powerful. In its initial development,""" Deumens et al. used END and treated the dynamics of the nuclei purely classical as in the above classical direct dynamics. More recently, a semiclassical description of the nuclear motion has been implemented by incorporating Heller s""" "" Gaussian wave packet dynamics."" ... 

Results of the counterintuitive pulse sequence. Shown, as function of time, are ed population of the wave packet of initial continuum states, population of u — 34, intermediate state, and population of v = 0, J = 0 final ground state. Dashed lines are y profiles of two Gaussian pulses whose central frequencies are oji = 18,143.775 cm-1 12,277.042 cm J (i.e, Aj = Ae = 0). The maximum intensity of the dump pulse jiflO8 W/cm2 and that of the pump pulse is 3.1 x 109 W/cm2. Both pulses last 8.5ns. i pHse peaks at t0 = 20 ns, the peak time of Na + Na wave packet. Dump pulse peaks f re that time. Initial kinetic energy of Na atoms is 0.0695 cm-1 (or 0.1 IC). (Taken g. 4, Ref. [345],)... 

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