Probability densities, permutational symmetry

Potential fluid dynamics, molecular systems, modulus-phase formalism, quantum mechanics and, 265—266 Pragmatic models, Renner-Teller effect, triatomic molecules, 618-621 Probability densities, permutational symmetry, dynamic Jahn-Teller and geometric phase effects, 705-711 Projection operators, geometric phase theory, eigenvector evolution, 16-17 Projective Hilbert space, Berry s phase, 209-210... 

A method to derive kinetic similar to (2.3.37), (2.3.43) has certain shortcomings. Say, Waite [84, 94, 95] has neglected the undistinguishabil-ity of similar reactants and related symmetry of the probability densities wm,m ( r m> OOm l 0 with respect to the permutation of coordinates in r m (or Accordingly, his approach is often called asymmetric ... 

Second, suitable solutions to the Schrodinger equation for electrons must have appropriate permutational symmetry. That is, an interchange of the space-spin coordinates Xj and Xj must not alter the probability density For this to be true, the interchange operator has to have the effect, = P. For... 

We will also find it useful to present densities that result from taking the energy derivative of sums of other subsets of the state-to-state reaction probabilities. Parity-specific densities can be obtained from the derivative of the sum of Pnn having the same parity P = (—l)7 (When 7 = 0, = /, and so P = +1.) Furthermore, for atom-diatom reactions of the form A + H2 - AH -I- H, we can define a spatial permutation symmetry S, which equals +1 for para hydrogen and —1 for ortho hydrogen. Symmetry-specific densities are obtained by summing those Pnn- with the same spatial permutation symmetry. Densities for a specific set (7, P, S) are denoted p,/ s when these are summed over P and S, the above densities p are obtained. 

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