Quasi-exactly solvable quartic potentials with centrifugal and Coulombic terms

D−dimensional central and complex potentials of a Coulomb plus quartic-polynomial form are considered in a PT −symmetrized radial Schrödinger equation. Arbitrarily large finite multiplets of bound states are shown obtainable in an elementary form. Relations between their energies and couplings are determined by a finite-dimensional secular equation. The Bender’s and Boettcher’s one-dimensional quasi-exact oscillators re-emerge here as the simplest chargeless solutions.