Quasi-exact minus-quartic oscillators in strong-core regime

PT-symmetric potentials V(x)=−x4+iBx3+Cx2+iDx+iF/x+G/x2 are quasi-exactly solvable, i.e., a specific choice of a small G=G(QES)=integer/4 is known to lead to wave functions ψ(QES)(x) in closed form at certain charges F=F(QES) and energies E=E(QES). The existence of an alternative, simpler and non-numerical version of such a construction is announced here in the new dynamical regime of very large G(QES)→∞.