Exact solvability of PDM systems with extended Lie symmetries

Abstract

It is shown that all PDM Schrodinger equations admitting more than five-dimensional Lie symmetry algebras (whose completed list can be found in paper [J.~Math. Phys. 58  (2017), 083508, 16 pp.] are exactly solvable. The corresponding exact solutions are presented. The supersymmetric aspects of the exactly solvable systems are discussed.