Turbiner's Conjecture in Three Dimensions
arXiv:math/0612621
Abstract
We prove a modified version of Turbiner's conjecture in three dimensions and we give a counter-example to the original conjecture. The Lie algebraic Schrödinger operators corresponding to flat metrics of a certain restricted type are shown to separate partially in either Cartesian, cylindrical or spherical coordinates.
29 pages, 8 figures