A tensorial theory of the higher-order constants of motion in quantum mechanics

A general theory of quantum mechanical constants of motion of arbitrary order in the momenta is developed. Because of rotational invariance the theory assumes an elegant tensorial form. The fundamental equations for the nth-order constants of motion in m variables are set up in Cartesian coordinates. To illustrate the use of the theory the 'anistropic oscillator' in two dimensions is discussed in detail, and all its constants of motion of second and third order are determined. (author)