Titlebook: Dimensional Scaling in Chemical Physics; Dudley R. Herschbach,John Avery,Osvaldo Goscinski Book 1993 Springer Science+Business Media Dordr

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Hyperspherical Symmetrye; and in both cases the solutions involve hyperspherical harmonics. In this section we shall discuss the close relationship between hyperspherical harmonics, harmonic polynomials, and exact D-dimensioanl hydrogenlike wave functions. We shall also discuss the importance of these functions in dimensi

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Hypercylindrical Symmetry the fixed orientation of the classical Kepler orbits. One focus is at the nucleus and the other a distance R away along the major axix of the elliptic orbit. Here we evaluate the separation constant α(n,m;ZR) and the coefficients g.(α) that specify the spheroidal eigenfunctions as hybrids of the fa

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General Computational Strategies1/D, is not a polynomial. The large-D limit appears to be an excellent qualitative model, but in order to accurately continue the solution from δ = 0 to δ = 1/3 it is necessary to take into account the functional form of E(δ) in that general region of the comples plane. The most important feature in

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Two-Electron Excited Statesthe three normal models of the Langmuir vibrations. Very accurate energies are obtained for the 1s2s states, which arise from excitation of the stretching vibrations. Reasonable, but somewhat less accurate, results are found for the energy of the 2p. resonance, which corresponds to excitation in the

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Nonseparable Dynamicsnamics. These “constants” belong to channels of excitation that point toward alternative fragmentations of the system but become identifiable only at sufficient distance from the system’s center of mass. It is shown how the nonseparability of channels originates in the critical transition from centr

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Pseudomolecular Electron Correlation in Atomsere we examine some new features of the adiabatic molecular problem illustrating the importance of motion near the saddle point of the two-centre potential. Properties of resonant states of the atomic three-body system are shown to be a direct consequence of this saddle-point motion. Its dimensional

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