Solvability in quantum mechanics and classically superfluous invariants

The author shows that in quantum mechanics there can be more commuting constants of motion than the dimension suggests. There will be an algebraic relationship between the invariants, but when this relationship is non-trivial it can be used to reduce the Schrodinger equation to quadratures. The Lame equation and some of its generalisations fall into the class of potentials for which this method works.