Abstract
We show that a suitable choice of the zero-order problem can lead directly to the emergence of non-Taylor expansions in ? for the ground-state energies of the Hamiltonian family H(?) = ??2 + r2 + ?/r? in regions ? ? 3. The discussion includes the role of dimension and the right order parameter. The effect of choosing a more general potential of the form r? + ?/r? is also considered.
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