By I. PRIGOGINE
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Additional info for ADVANCES IN CHEMICAL PHYSICS VOLUME 6
If this occurs, care must be taken that in the minimization of Eq. (81) the excited functions are orthogonal to those for the inner shells. Otherwise one will minimize to a fictitious energy representing a state in which all the electrons tend toward their separate ground states. 25 ANALYTIC THEORY OF CHEMICAL REACTIONS The application of Eq. (81) in the method of linear variation function^'^ is important for the later discussion in Sections III-A and III-B. , v= p c (82) It may then be shown using Eq.
1) Partial Waves What we are essentially looking for is the asymptotic behavior of the solution of Eq. (142) with V(r) = V ( r ) . In this event y 3 is a function only of 8 and r, as the scattering is symmetric about the polar axis z. But we delay consideration of the general spherically symmetric potential while we observe the effect of the simpler potential, V ( I )= 0, since the solution of the equation ( V2 + k2)yr= 0 (164) will be needed for comparison when V ( I )# 0. The eigenfunction for Eq.
DTa d n (190) Equation (190) is comparable to Eq. (178). The wave functions, however, are now stipulated by Eqs. (187) and (188), and the interaction potential is supplanted by terms from the small relative kinetic energy. One may treat Eq. (190) as we have Eq. (178), ignoring most of the nondiagonal elements in the series. It is important to understand, nevertheless, that even if such a procedure is adopted, the perturbed stationary-state wave functions still implicitly include some contribution from nondiagonal terms in the sense of Eq.
ADVANCES IN CHEMICAL PHYSICS VOLUME 6 by I. PRIGOGINE