How do supersingular perturbations generate non-Taylor series?

摘要

We show that a suitable choice of the zero-order problem can lead directly to the emergence of non-Taylor expansions in X for the ground-state energies of the Hamiltonian family H (lambda) = -del(2) + r(2) + lambda/r(beta) in regions beta >= 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(alpha) + lambda/r(beta) is also considered.