Quantum states of a sextic potential: hidden symmetry and quantum monodromy

A known terminating polynomial ansatz for a finite sub-set of states of the sextic central potential V(a, b, c; r) = ar(2) + br(4) + cr(6), c > 0, sub ject to integer related parameter constraints, is confirmed to apply in two as well as three dimensions. A hidden symmetry relating the eigenstates of V(a, b, c; r) to those of V(a, -b, c; r) is used to establish the boundary between the ansatz sub set and the infinite set of higher states. Connecti ons between the radial wavefunctions Ii, (a, b, c; r) and R-n'(a, -b, c; r) also provide semiclassical insight into the origin of the parameter constr aint. Finally the ansatz eigenvalue dispositions are related to the phenome non of quantum monodromy.