There is no two dimensional analogue of Lamé's equation (Q1195983)

The Lamé equation is a one-dimensional Schrödinger equation for which all Bloch eigenvalues and multipliers can be explicitly parametrized by meromorphic functions defined on a compact Riemann surface. The authors prove the non-existence of an analogous equation in the two-dimensional case. The work contains some interesting results which, one hopes, will help the development of some precise methods for solving Schrödinger's equations corresponding to actual physical systems.