Angular wavepackets

Angular wavepackets excited by the full multipolar interaction,... 

Figure 2. Wavepacket dynamics of the H + H H2 + H scattering reaction, shown as snapshots of the density (wave packet amplitude squard) at various times, The coordinates, in au, are described in Figure la, and the wavepacket is initially moving to describe the H atom approaching the H2 molecule. The density has been integrated over the angular coordinate, The PES is plotted for the collinear interaction geometry, 0 180, ...

A mixed DVR (discrete variable representation)43 for all the radial coordinates and basis set representations for the angular coordinates are used in the wavepacket propagation.44... 

As discussed for several decades by a number of authors, the nature of light and photon physics is related not only to the propagation of plane wavefronts but also to axisymmetric wavepackets, the concepts of a rest mass, a magnetic field in the direction of propagation, and an associated angular momentum (spin). 

The result (173) applies to a photon model with the angular momentum h/2n of a boson, whereas the photon radius r would become half as large for the angular momentum h/4 of a fermion. Moreover, the present analysis on superposition of EMS normal modes is applicable not only to narrow linewidth wavepackets but also to a structure of short pulses and soliton-like waves. In these latter cases the radius in Eq. (173) is expected to be replaced by an average value resulting from a spectrum of broader linewidth. 

At this point a question arises as to the possibility of having an expression for the angular momentum also in the rest frame K. However, such a question is not simple, because the definition of a Poynting vector in the rest frame of the wavepacket is not straightforward. 

These questions appear to be understandable in terms of both photon models. The wavepacket axisymmetric model has, however, an advantage of being more reconcilable with the dot-shaped marks finally formed by an individual photon impact on the screen of an interference experiment. If the photon would have been a plane wave just before the impact, it would then have to convert itself during the flight into a wavepacket of small radial dimensions, and this becomes a less understandable behavior from a simple physical point of view. Then it is also difficult to conceive how a single photon with angular momentum (spin) could be a plane wave, without spin and with the energy hv spread over an infinite volume. Moreover, with the plane-wave concept, each individual photon would be expected to create a continuous but weak interference pattern that is spread all over the screen, and not a pattern of dot-shaped impacts. 

Figure 1. Intramolecular vibrational density redistribution IVR of Na3

We show how one can image the amplitude and phase of bound, quasibound and continuum wavefunctions, using time-resolved and frequency-resolved fluorescence. The case of unpolarized rotating molecules is considered. Explicit formulae for the extraction of the angular and radial dependence of the excited-state wavepackets are developed. The procedure is demonstrated in Na2 for excited-state wavepackets created by ultra-short pulse excitations. 

The functions (r. R.O.t = 0) involve a product of the initial wavefunction and the internal coordinate dejjendent vector components of the transition dipole moment (see Ref. [43] and Appendix B of Ref. [33] ). As the total angular momentum is a conserved quantity during the time propagation of the wavepacket, we may divide up the initied wavepacket (Eq. (23)) into three components [43], one for each of the allowed valuers of J. Thus E(p (23) may be rewritten as ... 

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