Coordinate systems adapted to constants of motion

Abstract

We present some examples of mechanical systems such that given $n$ constants of motion in involution (where $n$ is the number of degrees of freedom), we can identify a coordinate system in which the Hamilton--Jacobi equation is separable (or $R$-separable), with the separation constants being the values of the given constants of motion. Analogous results for the Schrödinger equation are also given.