  We apply the quantum mechanical (first-quantized) JWKB approximation to a
two-body path integral describing the near-forward scattering of two
relativistic, heavy, non-identical, scalar particles in $D$ spacetime
dimensions. In contrast to the loop expansion, in $D = 4$ this gives a
strong-coupling expansion, and in $D = 3$ a non-perturbative weak-coupling
expansion. When the interaction is mediated by massless quanta with spin $N$,
we obtain explicit, relativistic results for the scattering amplitude when $N =
0$, $1$ and $2$. In $D = 4$ we find a Regge trajectory function that agrees
with the usual quantum mechanical spectrum. We also find an exponentiated
infrared divergence that becomes a pure phase factor when the Mandelstam
invariants $s$ and $t$ are inside of the physical scattering region. In $D = 3$
we find a singularity whose position along the $s$ axis is dependent on $t$.
When the interaction is mediated by a heavy scalar with mass $M$, in $D = 3$ we
find an all-order scattering amplitude where the multi-mass branch points $t =
(L + 1)^{2}M^{2}$ appear as Regge poles.
