Auxiliary quantization constraints on the von Roos ordering-ambiguity at zero binding energies; azimuthally symmetrized cylindrical coordinates

TL;DR

This paper explores how zero-energy quantum states influence the von Roos Hamiltonian with position-dependent mass in cylindrical coordinates, revealing auxiliary constraints on ordering ambiguity parameters and aiding separability.

Contribution

It demonstrates that zero-energy states provide additional separability options and impose new constraints on the von Roos Hamiltonian's ambiguity parameters.

Findings

Zero-energy states enable feasible separability of the Hamiltonian.

Auxiliary constraints on ambiguity parameters are derived.

The approach uses azimuthally symmetrized cylindrical coordinates.

Abstract

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.