By I. Prigogine, Stuart A. Rice
Advances in Chemical Physics covers fresh advances on the innovative of study relative to chemical physics. The sequence, Advances in Chemical Physics, offers a discussion board for severe, authoritative reviews of advances in each zone of the self-discipline.
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Additional info for Advances in Chemical Physics, Vol.125 (Wiley 2003)
Kato  showed that these series have a nonzero radius of convergence. This radius is determined by the distance from the origin to the nearest singularity in the complex plane lÃ . The study of the radius of convergence, lÃ , and whether or not this is the same as the critical value of lc , has a long history with controversial results [98–101]. Recently, Morgan and co-workers  have performed a 401-order perturbation calculation to resolve this controversy over the radius of convergence of the l ¼ 1=Z expansion for the ground-state energy.
5 Re(E) Figure 18. ImðEÞ versus ReðEÞ for complex-rotated N ¼ 100 diagonalization of Hamiltonian equation (101), with a ¼ 0:2, J ¼ 0:2, f ¼ p=10 (circles), and f ¼ p=5 (crosses). The continuous line occurs for an angle f with the real axis, the first (sharp) resonance appears for both calculations, and the second resonance appears only for f ¼ p=5 > y1. finite-size scaling for atomic and molecular systems 57 show all the eigenvalues for f ¼ p=10 and f ¼ p=5 obtained with a complexrotated 500-function expansion.
As one should expect, there is a discontinuity in the first derivative as a function of l . 10 1/N Figure 4. lðNÞ as a function of 1=N for the ground state of the Yukawa potential. The extrapolated values are shown by dots. D. Data Collapse for the Schro¨dinger Equation In order to show the data collapse for quantum few-body problems, let us examine the main assumption we have made in Eq. (60) for the existence of a scaling ðNÞ function for each truncated magnitude hOil with a unique scaling exponent n.