Electron wave packet

The eigenvectors are positive and negative combinations of 4 and Ta, respectively. f d ( Fa) is a wave function where the mobile electron is at the donor (acceptor). In a time dependent theory, the wave function is set equal to at t=0. The electronic wave packet moves across the barrier to the acceptor. Landau-Zener theory [23,24] provides the probability for crossing to the upper surface at the avoided crossing ... 

It is clear that a core-hole represents a very interesting example of an unstable state in the continuum. It is, however, also rather complicated [150]. A simpler system with similar characteristics is a doubly excited state in few-body systems, as helium. Here, it is possible [151-153] to simulate the whole sequence of events that take place when the interaction with a short light pulse first creates a wave packet in the continuum, including doubly excited states, and the metastable components subsequently decay on a timescale that is comparable to the characteristic time evolution of the electronic wave packet itself. On the experimental side, techniques for such studies are emerging. Mauritsson et al. [154] studied recently the time evolution of a bound wave packet in He, created by an ultra-short (350 as) pulse and monitored by an IR probe pulse, and Gilbertson et al. [155] demonstrated that they could monitor and control helium autoionization. Below, we describe how a simulation of a possible pump-probe experiment, targeting resonance states in helium, can be made. 

N. Choi, T. Jiang, T. Morishita, M.-H. Lee, C.D. Lin, Theory of probing attosecond electron wave packets via two-path interference of angle-resolved photoelectrons, Phys. Rev. A 82 (2010) 013409. 

Alber, G. and Zoller, P. (1991). Laser excitation of electronic wave packets in Rydberg atoms, Phys. Rep. 199, 231-280. 

The group velocity of de Broglie matter waves are seen to be identical with particle velocity. In this instance it is the wave model that seems not to need the particle concept. However, this result has been considered of academic interest only because of the dispersion of wave packets. Still, it cannot be accidental that wave packets have so many properties in common with quantum-mechanical particles and maybe the concept was abandoned prematurely. What it lacks is a mechanism to account for the appearance of mass, charge and spin, but this may not be an insurmountable problem. It is tempting to associate the rapidly oscillating component with the Compton wavelength and relativistic motion within the electronic wave packet. 

We are also interested in the effects of small applied fields imagine the electron wave packet described above, but now allow a weak, slowly varying potential K(r) to be present. The packet will work against this potential at the rate v dF/dr This energy can only come from the band energy of the electron, througli a change, with time, of the central wave number kg of the packet ... 

The condition of applicability of the classical approach can be derived considering the energy loss to the electron wave packet. The uncertainty in transferred energy is due to uncertainty of the impact parameter s and it is determined by the width of the wave packet 8s. At s > a when the classical impulse approach is applicable T = the resulting relative... 

Gor kov and Eliashberg investigated the problem of a size-induced metal-insulator transition in terms of the location of the gas of conduction electrons in a metal through the (finite) size-induced confinement of the electron wave packet. The de Broglie wavelength X of electrons is given by ... 

In this chapter we present an accurate and flexible method for the numerical simulation of the evolution of electronic wave-packets in alkah atoms. As a testing ground for our approach we calculated the dynamics of Stark wave-packets in cesium for different electric field strengths. The agreement with recent experimental results is demonstrated, and especially the influence of the electric field strength and the core-scattering on the recurrence spectra is reproduced accurately. 

K. Harumiya, 1. Kawata, H. Kono, Y. Fujimura, Exact two-electron wave packet dynamics of H2 in an intense laser field Formation of localized ionic states H+H , J. Chem. Phys. 113 (2000) 8953. 

Substituting m = h/c c, gives V, = ficAc/47rr, anywhere within the sphere. This corresponds to the potential energy of a spherical electronic wave packet... 

A. Wolde, I.D. Noordam, H.G. MiiUer, A. Lagendijk, H.B. van Linden, Observation of radially localized atomic electron wave packets. Phys. Rev. Lett. 61, 2099 (1988)... 

Periyasamy G, Levine R, Remade F (2009) Electronic wave packet motion in water dimer cation a many electron description. Chem Phys 366 129-138... 

If electronic wave packets are going to behave as particles, their wave packets must have properties like velocity and acceleration. A wave packet is not necessarily an eigenfunction to the operator related to a certain property or observable, for example, angular momentum or kinetic energy. A distribution of values is observed. The expectation value is defined as a kind of average value for the region of space where the electron can be found ... 

The Interplay of Nuclear and Electron Wave packet Motion in the Control... 

Ando K (2012) Electron wave packet modeling of chemical bonding Floating and breathing minimal packets with perfect-pairing valence-bond spin coupling. Chem Phys Lett 523 134— 138... 

During this lecture I hope I impressed you with the fact that an electron in a fluid like Ar is bound, its wave function is extended, and, in a "frozen" liquid (without thermal motion of the atoms), the electron in the conduction band would not scatter, i.e., it would be in a stationary state. Scattering corresponds to a transition from one stationary state to another. It is not the result of the interaction with a single atom but instead with a change of potential brought about by the displacement of the atoms of the fluid. This can be described by phonons, if we consider their time dependence (usually in the GHz range), or "static" if we consider a much slower time dependence so that the electron wave packet (whose dimensions are of the order of the thermal wave length of the electron, A = moved far from the... 

Fig. 1. Quantitites characterizing the electron-lithium ion recombination in liquid ammonia as a function of f. (a) R, the electron wave packet size, (b) Q, the net charge within 3 A of the Li" " ion.

As in wave mechanics, the simulation of chemical phenomena by number theory is characterized by the appearance of integers, in this case associated with chemical structures and transformations. An obvious conclusion is that the elementary units of matter should be viewed as wave structures rather than point particles, which is consistent with the first appearance of matter in curved space-time. Even 3D wave packets behave in a manner convincingly like ponderable matter and rationalize the equivalence of mass and energy in a natural way. There is no compelling reason why this simple model should be concealed with the notion of wave/particle duality and more so on realizing that the wave-like space-time distortions are strictly 4D structures. In response to environmental pressure, an electronic wave packet can shrink to the effective size of an elementary particle or increase to enfold a proton as a spherical standing wave. 

Table 10 Relative volumes, (in units of = Og on the //-scale), of unit-electron wave packets at various atomic sublevels...

These ionization radii, which have been shown [19] to underpin the electronegativity concept, have recently been derived by an extremely simple and more reliable simulation of atomic structure as a standing electronic wave packet [6]. This simulation, which is free of the errors of approximation that affect the HF simulation of small atoms, has produced a more reliable set of ionization radii, suitable for direct prediction of interatomic distance in general pairwise interaction within bonds of any order. The procedure is outlined in the next section. 

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