Quasi-exact solvability
A linear differential operator L is called quasi-exactly-solvable (QES) if it has a finite-dimensional invariant subspace of functions { V } n {\displaystyle \{{\mathcal {V}}\}_{n}} such that L : { V } n → { V } n , {\displaystyle L:\{{\mathcal {V}}\}_{n}\rightarrow \{{\mathcal {V}}\}_{n},} where n is a dimension of { V } n {\displaystyle \{{\mathcal {V}}\}_{n}} . There are two important cases: { V } n {\displaystyle \{{\mathcal {V}}\}_{n}} is the space of multivariate polynomials of degree not higher than some integer number; and { V } n {\displaystyle \{{\mathcal {V}}\}_{n}} is a subspace of a Hilbert space.