  The surprising divergence of the expectation value $<\!p^6\!>$ for the square
well potential is known. Here, we prove and demonstrate the divergence of
$<\!p^6\!>$ in potential wells which have a finite jump discontinuity; apart
from the square-well two-piece half-potentials wells are examples. These
half-potential wells can be expressed as $V(x)=-U(x) \Theta(x)$, where
$\Theta(x)$ is the Heaviside step function. $U(x)$ are continuous and
differentiable functions with minimum at $x=0$ and which may or not vanish as
$x\sim \infty$.
