The semiclassical approximation fur a quantum amplitude is given by the sum
of contributions from intersections of the appropriate manifolds in classi
cal phase space. The intersection overlaps are just the Van Vleck, determin
ants multiplied by a phase given by a classical action. Here we consider tw
o nonstandard instances of this semiclassical prescription which would appe
ar to be on shaky ground, yet the corresponding physical situations are not
unusual. The first case involves momentum-space WKB theory fur scattering
potentials; the second is a propagator for the whisker map that arises in g
eneric two-dimensional systems. In the former case two manifolds become asy
mptotically tangent, and the semiclassical formula needs to he uniformized
in order to give a meaningful wave function. We give a uniformization proce
dure. In the latter case, there are an infinite number of intersections in
phase space within a zone with the area of Planck's constant (the limit of
resolution for quantum mechanics), yet the semiclassical sum over all contr
ibutions is shown to be correct.