AUXILIARY QUANTIZATION CONSTRAINTS ON THE VON ROOS ORDERING-AMBIGUITY AT ZERO BINDING ENERGIES; AZIMUTHALLY SYMMETRIZED CYLINDRICAL COORDINATES

Using azimuthally symmetrized cylindrical coordinates, we report the consequences of zero-energy quantal states on the von Roos Hamiltonian. A position-dependent mass (PDM) M(ρ, φ, z) = bzjρ2υ+1/2 is used. We show that the zero-energy setting not only offers an additional degree of freedom toward feasible separability for the von Roos Hamiltonian, but also manifestly yields auxiliary quantized ambiguity parametric constraints (i.e. the ambiguity parameters are given in terms of quantum numbers).