Quasi-Classical 1/ N Energy Formulae for the Superposition Between the Attractive Potential -λ 0 / x 2 and the Repulsive ( n > 2)-Potential γ( n )/ x n

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Abstract
Nonrelativistic energy formulae for the superposition between the attractive potential - λ0/x2 and the repulsive n > 2-potential γ(n)/xn have been established in N space dimensions, both to first and second order in 1/N. One proceeds by combining the analytic continuation towards n > 2 of 1/N energy results obtained previously for n < 2-Hamiltonians, with additional selection criteria implied by the related WKB-description. This leads to well-defined energy-levels relying on supercritical λ0-values. Finally, we find the 1/N energy formula for a spinless relativistic two-body system, which is subject to the attractive scalar potential - Λ0/x2.