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

Divergence of $\langle p^6\rangle$ in discontinuous potential wells