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

Abstract

PT-symmetric potentials $V({x}) = -{x}^4 +jB {x}^3 + C {x}^2+jD {x} +jF/{x} +G/{x}^2$ 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 $G^{(QES)} \to \infty$.