  Earlier, potentials like square well and several other half-potential wells
with discontinuous jump have been found to have the expectation value $<\! p^6
\!>$ to be divergent for all bound states. Here, we consider two-piece
symmetric potential wells to prove and demonstrate that in them the expectation
value of $p^6$ diverges for even states and converges for odd states. Here, $p$
denotes momentum. We also present three exactly solvable models.
