Particle exchange

Equality between the 1, 2 wave function and the modulus of the 2, 1 wave function, v /(j2, i), shows that they have the same curve shape in space after exchange as they did before, which is necessary if their probable locations are to be the same. The phase factor orients one wave function relative to the other in the complex plane, but Eq. (9-17) is simplified by one more condition that is always true for particle exchange. When exchange is canied out twice on the same particle pair, the operation must produce the original configuration of particles... 

Thus the atmospheric component of the planet s radiation budget is strongly modulated by the indirect effects of oceanic gas and particle exchange. As will be... 

Until very recently, however, the same could not be said for reactive systems, which we define to be systems in which the nuclear wave function satisfies scattering boundary conditions. It was understood that, as in a bound system, the nuclear wave function of a reactive system must encircle the Cl if nontrivial GP effects are to appear in any observables [6]. Mead showed how to predict such effects in the special case that the encirclement is produced by the requirements of particle-exchange symmetry [14]. However, little was known about the effect of the GP when the encirclement is produced by reaction paths that loop around the CL... 

So far, we have treated the atoms as distinguishable particles, both in the general theory of Section II and in the application to H + H2 in Section III. Here, we explain how to incorporate the effects of particle exchange symmetry. First, we discuss how the symmetry of the system maps from the physical onto the double space, and then explain what effect the GP has on wave functions of reactions that (like H + H2) have identical reagents and products. 

Hentschke, R. Bast, T. Aydt, E. Kotelyanskii, M., Gibbs-ensemble molecular dynamics a new method for simulations involving particle exchange, J. Mol. Model. 1996, 2, 319-326... 

Ideal gas particles exchange energy only by means of perfectly elastic collisions — collisions in which the total kinetic energy of the particles remains constant. 

The second transformation is again Schofield s, and the first one has been added to assure the exact reproduction of the quantum mechanical ideal gas behavior if particles exchange symmetry effects may be neglected [318, 286]. 

The three main processes by which atmospheric deposition of pesticides to the lakes occurs are wet deposition (rain and snow), dry deposition (particulates), and air-water gas exchange. For many of the banned pesticides, gas exchange across the air-water interface, in particular, is often the dominant deposition process, when compared with precipitation and dry particle exchange [42-44], The physicochemical considerations, as well as descriptions of calculation models for atmospheric deposition to lakes, rivers, and the oceans, have been reviewed extensively [45-47]. 

First, in common with any simulation of open systems, it runs into increasing difficulties as one moves down the coexistence curve to the region of high densities where particle insertion (entailed by particle exchange) has a low acceptance probability. 

If switching the coordinates of two of the particles leaves the function unchanged, it is said to be symmetric with respect to particle exchange, while if the function changes sign it is said to be antisymmetric with respect to particle... 

In the procedure just outlined, the final wave function retains the proper symmetry under exchange of state indices or particle exchange. This wave function, described in more detail below, corresponds to a particular partition of the particles into pairs, and each of the pairs is associated with every possible two- particle state that can be formed by and evolves out of an original set of single-particle free and non-interacting states. Denoting by a zero subscript two-particle states in free space, we have the following orthonormality... 

There is no simple device which enables the measurement of dry deposition in a manner as convenient as for wet deposition. Instead, comparatively less direct methods must be used, none of which is fully proven as yet. For particle exchange, leaf-washing and through-fall techniques (1) can provide measurements of the accumulated deposit on natural surfaces. Likewise, accumulation on snow surfaces can be sampled, and subjected to subsequent chemical analysis. It is evident, however, that such methods only apply in certain circumstances. Budget techniques are sometimes advocated, such as in the case of calibrated watersheds, but these have rarely delivered unequivocal results. The difficulty that arises is that the dry deposition must necessarily be computed as the difference between poorly determined in-flow and out-flow measurements. These, and. a wide variety of other experimental methods, have been reviewed elsewhere (2). 

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