Nonsingular spiked harmonic oscillator

Abstract

A perturbative study of a class of nonsingular spiked harmonic oscillators defined by the Hamiltonian H=−d2/dr 2+r 2+λ/r α in the domain [0,∞] is carried out, in the two extremes of a weak coupling and a strong coupling regimes. A path has been found to connect both expansions for α near 2.