The conserved operators generated by a solution of the Schrödinger equation

Abstract

It is shown that, in a similar manner as a complete solution of the Hamilton--Jacobi equation for a system with $n$ degrees of freedom yields $2n$ constants of motion, each solution of the Schrödinger equation containing $n$ parameters leads to $2n$ operators that are constants of motion; these $2n$ operators form two sets of $n$ mutually commuting operators.