The theory of the Weyl-Titchmarsh m function for second-order ordinary differential operators in generalized and applied to partial differential operators of the form - Δ + q(x) acting in three space dimensions. Weyl operators M(z) are defined as maps from L² (S₁) to L² (S₁) (S₁ ≡ unit sphere in R³) for exterior and interior boundary value problems, and for the partial differential operator acting in L² (R³), with the standard Weyl-Titchmarsh m function recovered in the special case that q is spherically symmetric. The analysis is carried out rather explicity, allowing for the determination of precise norm bounds for M operators and for the proof of higher dimensional analogues of a number of the fundamental results of standard Weyl-Titchmarsh theory.