“…We are attempting to establish theoretical basis to mathematically analyze these systems, with a key goal of identifying observables that are provable verifiably with experimental techniques, such as the quantum vacuum -optic flux viewer Ferrolens to probe inside the ferro vacuum materials, as well as Bose -Einstein condensate that can detect polar -core spin vortices especially of Dirac monopole. Standard techniques established by vast amount of quantum physics literature on constructing, analyzing, interpreting, quantifying as well as problem solving eigenvalues, eigen matrices, eigenvectors, and fields of Hermitian and/or non -Hermitian Hamiltonian operator [36][37][38][39][40][41][42][43][44][45] generating characteristic energy and field spectrum are widely utilized to configure characterization of quantum vortex systems considered here. In all theoretical endeavors, matrix rules and quantifiable formulations follow integrated procedures that are adapted from the research of physics literature articles, samples of which appear in the reference list, with [44][45][46][47][48]62,64,67 in this paper.…”