General Space-Momentum Commutation Relation

Abstract

This paper derives the general commutator [q^m, pⁿ] for all integers m and n, positive or negative. Two new identities for the binomial coefficients are derived using the general commutator. A simple example of the use of the general commutation relation is given in the expansion of (Ap + Bq)ⁿ (A, B, constants) in normal form for integer n.