Scaling relations for multiplicative quantum mechanical operators

Scaling relations are derived for the matrix elements of a multiplicative quantum mechanical operator. While the relations have been set down earlier, the present derivation is, we believe, more transparent. In order to satisfy certain attractive properties, the coefficients in these relations have previously been identified as the principal values of improper integrals. We show here, however, that the scaling relations can be rewritten in terms of scaling coefficients which are given as proper integrals and which satisfy the same attractive properties.