  Perfectly conducting boundaries, and their Dirichlet counterparts for quantum
scalar fields, predict nonintegrable energy densities. A more realistic model
with a finite ultraviolet cutoff yields two inconsistent values for the force
on a curved or edged boundary (the "pressure anomaly"). A still more realistic,
but still easily calculable, model replaces the hard wall by a power-law
potential; because it involves no a posteriori modification of the formulas
calculated from the theory, this model should be anomaly-free. Here we first
set up the formalism and notation for the quantization of a scalar field in the
background of a planar soft wall, and we approximate the reduced Green function
in perturbative and WKB limits (the latter being appropriate when either the
mode frequency or the depth into the wall is sufficiently large). Then we
display numerical calculations of energy density and pressure for the region
outside the wall, which show that the pressure anomaly does not occur there.
Calculations inside the wall are postponed to later papers, which must tackle
regularization and renormalization of divergences induced by the potential in
the bulk region.
