  Using azimuthally symmetrized cylindrical coordinates, we report the
consequences of zero-energy quantal states on the von Roos Hamiltonian. A
position-dependent mass M({\rho},\phi,z)=bz^{j}{\rho}^{2\u{psion}+1}/2 is used.
We show that the zero-energy setting not only offers an additional degree of
freedom towards feasible separability for the von Roos Hamiltonian, but also
manifestly yields auxiliary quantized ambiguity parametric constraints.
